This extraordinary volume contains a large part of the mathematical correspondence between A. Grothendieck and J.-P. Serre. It forms a vivid introduction to the study of algebraic geometry during the years 1955-1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. In the book...
This extraordinary volume contains a large part of the mathematical correspondence between A. Grothendieck and J.-P. Serre. It forms a vivid introduction to the study of algebraic geometry during the years 1955-1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. In the book, the reader can follow the creation of some of the most important notions of modern mathematics, such assheaf cohomology, schemes, Riemann-Roch type theorems, algebraic fundamental group, motives, etc. The letters also reflect the mathematical and political atmosphere of this period (Bourbaki, Paris, Harvard, Princeton, war in Algeria, etc.). Also included are letters written between 1984 and 1987. Theletters are supplemented by J-P.Serre's notes, which give explanations, corrections, and references to further results. The book is a unique bilingual (French and English) volume. The original French text is supplemented here by the English translation, with French text printed on the left-hand pages and the corresponding English text printed on the right. The book also includes several facsimiles of original letters. The original French volume was edited by Pierre Colmez and J-P. Serre. TheEnglish translation for this volume was translated by Catriona Maclean and edited by J-P. Serre and Leila Schneps. The book should be useful to specialists in algebraic geometry, mathematical historians, and to all mathematicians who want to experience the unfolding of great mathematics.
Somewhere, you describe your approach to mathematics, in which one does not attack a problem head-on, but one envelopes and dissolves it in a rising tide of general theories. Very good: this is your way of working, and what you have done proves that it does indeed work. For topological vector spaces or algebraic geometry, at least... It is not so clear for number theory (in which the structures involved are far from obvious---or rather, in which all possible structures are involved); I have the same reservation for the theory of modular forms, which is visibly richer than its simple "Lie groups" aspect or its "algebraic geometry---moduli schemes" aspect. Whence this question: did you not come, in fact, around 1968-1970, to realize that the "rising tide" method was powerless against this ty... (查看原文)
Next year, I hope to get a satisfactory theory of the fundamental group, and finish up the writing of chapters Ⅳ, Ⅴ, Ⅵ, Ⅶ (the last one being the fundamental group) at the same time as categories. In two years, residues, duality, intersections, Chern, and Riemann-Roch. In three years, Weil cohomology, and a little homotopy, God willing. In between, I don't know when, the "big existence theorem" with Picard etc., some algebraic curves, and abelian schemes. Unless there are unexpected difficulties or I get bogged down, the multiplodocus should be ready in 3 years time, or 4 at the outside. WE WILL THEN BE ABLE TO START DOING ALGEBRAIC GEOMETRY!
(查看原文)
局部有方程和坐标，而整体没有方程。研究代数几何，依据代数，不要被几何所误导。Grothendieck的风格不看方程，直接从整体（嵌入）开始-从导出函子开始用同调代数表示一切： "Mittag-Leffler"逼近过程lim作为导出函子, Cartan's theorems A and B （szyzygytic resolutions）作为其特例,
局部有方程和坐标，而整体没有方程。研究代数几何，依据代数，不要被几何所误导。Grothendieck的风格不看方程，直接从整体（嵌入）开始-从导出函子开始用同调代数表示一切： "Mittag-Leffler"逼近过程lim作为导出函子, Cartan's theorems A and B （szyzygytic resolutions）作为其特例,
serre在给grothendieck的回信中说： one thing strikes me in the texts that i have seen：you are surprised and indignant that your former students did not continue the work which you had undertaken and largely completed. but you do not ask the most obvious que...
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Serre to Grothendieck, 1986 Somewhere, you describe your approach to mathematics, in which one does not attack a problem head-on, but one envelopes and dissolves it in a rising tide of general theories. Very good: this is your way of working, and what you have done proves that it does indeed work. For topological vector spaces or algebraic geometry, at least... It is not so clear for number the...
2012-09-13 11:26
Serre to Grothendieck, 1986
Somewhere, you describe your approach to mathematics, in which one does not attack a problem head-on, but one envelopes and dissolves it in a rising tide of general theories. Very good: this is your way of working, and what you have done proves that it does indeed work. For topological vector spaces or algebraic geometry, at least... It is not so clear for number theory (in which the structures involved are far from obvious---or rather, in which all possible structures are involved); I have the same reservation for the theory of modular forms, which is visibly richer than its simple "Lie groups" aspect or its "algebraic geometry---moduli schemes" aspect. Whence this question: did you not come, in fact, around 1968-1970, to realize that the "rising tide" method was powerless against this type of question, and that a different style would be necessary--- which you did not like? 引自第250页
J'ai d'ailleurs pris la décision de prendre ma retraite l'an prochain (j'aurai alors soixante ans), pour me sentir plus libre de poursuivre dans une direction qui ne s'insère dans aucune discipline reconnue d'utilité publique et subventionnable comme telle, et où je suis le seul à m'engager.
2014-09-11 17:31
J'ai d'ailleurs pris la décision de prendre ma retraite l'an prochain (j'aurai alors soixante ans), pour me sentir plus libre de poursuivre dans une direction qui ne s'insère dans aucune discipline reconnue d'utilité publique et subventionnable comme telle, et où je suis le seul à m'engager.
i am trying to learn things, but there is so much to look at and it is so slow. Cartier seems to be an amazing person, especially his speed of understanding, and the incredible amount of things he reads and grasps; I really have the impression that in a few years he will be where you are now. I am exploiting him most profitably.
2012-11-23 15:14
i am trying to learn things, but there is so much to look at and it is so slow.
Cartier seems to be an amazing person, especially his speed of understanding, and the incredible amount of things he reads and grasps; I really have the impression that in a few years he will be where you are now. I am exploiting him most profitably.引自第20页
Grothendieck on the military service: I do not think that the danger of losing one's life is such, at this point, that it has become more important than the loss of two years of training (for any young person, scientist or otherwise), leaving aside entirely the moral question (to which most people are apparently indifferent). The minimal probability of being killed does not seem to me to make a...
2012-09-12 19:33
Grothendieck on the military service:
I do not think that the danger of losing one's life is such, at this point, that it has become more important than the loss of two years of training (for any young person, scientist or otherwise), leaving aside entirely the moral question (to which most people are apparently indifferent). The minimal probability of being killed does not seem to me to make a big difference. On the other hand, if certain Academics brought the effects of military service (and, by implication, of the Algerian war) on the scientific level of the country to the attention of the public and the authorities, and required some reforms, it would not exclude the possibility of classical scholars, technicians, firemen and lamp-lighters grouping together to require analogous reforms for themselves, on analogous and to my mind equally valid grounds. Any action in this direction, even if very limited, will contribute to making people realize the consequences of the militarization of the country, and might create a precedent for analogous and vaster actions.
引自第128页
i am trying to learn things, but there is so much to look at and it is so slow. Cartier seems to be an amazing person, especially his speed of understanding, and the incredible amount of things he reads and grasps; I really have the impression that in a few years he will be where you are now. I am exploiting him most profitably.
2012-11-23 15:14
i am trying to learn things, but there is so much to look at and it is so slow.
Cartier seems to be an amazing person, especially his speed of understanding, and the incredible amount of things he reads and grasps; I really have the impression that in a few years he will be where you are now. I am exploiting him most profitably.引自第20页
The famous Declaration of Grothendieck reads like this: Next year, I hope to get a satisfactory theory of the fundamental group, and finish up the writing of chapters Ⅳ, Ⅴ, Ⅵ, Ⅶ (the last one being the fundamental group) at the same time as categories. In two years, residues, duality, intersections, Chern, and Riemann-Roch. In three years, Weil cohomology, and a little homotopy, God willing...
2012-09-12 17:10
The famous Declaration of Grothendieck reads like this:
Next year, I hope to get a satisfactory theory of the fundamental group, and finish up the writing of chapters Ⅳ, Ⅴ, Ⅵ, Ⅶ (the last one being the fundamental group) at the same time as categories. In two years, residues, duality, intersections, Chern, and Riemann-Roch. In three years, Weil cohomology, and a little homotopy, God willing. In between, I don't know when, the "big existence theorem" with Picard etc., some algebraic curves, and abelian schemes. Unless there are unexpected difficulties or I get bogged down, the multiplodocus should be ready in 3 years time, or 4 at the outside. WE WILL THEN BE ABLE TO START DOING ALGEBRAIC GEOMETRY!
引自第83页
Grothendieck on the military service: I do not think that the danger of losing one's life is such, at this point, that it has become more important than the loss of two years of training (for any young person, scientist or otherwise), leaving aside entirely the moral question (to which most people are apparently indifferent). The minimal probability of being killed does not seem to me to make a...
2012-09-12 19:33
Grothendieck on the military service:
I do not think that the danger of losing one's life is such, at this point, that it has become more important than the loss of two years of training (for any young person, scientist or otherwise), leaving aside entirely the moral question (to which most people are apparently indifferent). The minimal probability of being killed does not seem to me to make a big difference. On the other hand, if certain Academics brought the effects of military service (and, by implication, of the Algerian war) on the scientific level of the country to the attention of the public and the authorities, and required some reforms, it would not exclude the possibility of classical scholars, technicians, firemen and lamp-lighters grouping together to require analogous reforms for themselves, on analogous and to my mind equally valid grounds. Any action in this direction, even if very limited, will contribute to making people realize the consequences of the militarization of the country, and might create a precedent for analogous and vaster actions.
引自第128页
Serre to Grothendieck, 1986 Somewhere, you describe your approach to mathematics, in which one does not attack a problem head-on, but one envelopes and dissolves it in a rising tide of general theories. Very good: this is your way of working, and what you have done proves that it does indeed work. For topological vector spaces or algebraic geometry, at least... It is not so clear for number the...
2012-09-13 11:26
Serre to Grothendieck, 1986
Somewhere, you describe your approach to mathematics, in which one does not attack a problem head-on, but one envelopes and dissolves it in a rising tide of general theories. Very good: this is your way of working, and what you have done proves that it does indeed work. For topological vector spaces or algebraic geometry, at least... It is not so clear for number theory (in which the structures involved are far from obvious---or rather, in which all possible structures are involved); I have the same reservation for the theory of modular forms, which is visibly richer than its simple "Lie groups" aspect or its "algebraic geometry---moduli schemes" aspect. Whence this question: did you not come, in fact, around 1968-1970, to realize that the "rising tide" method was powerless against this type of question, and that a different style would be necessary--- which you did not like? 引自第250页
J'ai d'ailleurs pris la décision de prendre ma retraite l'an prochain (j'aurai alors soixante ans), pour me sentir plus libre de poursuivre dans une direction qui ne s'insère dans aucune discipline reconnue d'utilité publique et subventionnable comme telle, et où je suis le seul à m'engager.
2014-09-11 17:31
J'ai d'ailleurs pris la décision de prendre ma retraite l'an prochain (j'aurai alors soixante ans), pour me sentir plus libre de poursuivre dans une direction qui ne s'insère dans aucune discipline reconnue d'utilité publique et subventionnable comme telle, et où je suis le seul à m'engager.
i am trying to learn things, but there is so much to look at and it is so slow. Cartier seems to be an amazing person, especially his speed of understanding, and the incredible amount of things he reads and grasps; I really have the impression that in a few years he will be where you are now. I am exploiting him most profitably.
2012-11-23 15:14
i am trying to learn things, but there is so much to look at and it is so slow.
Cartier seems to be an amazing person, especially his speed of understanding, and the incredible amount of things he reads and grasps; I really have the impression that in a few years he will be where you are now. I am exploiting him most profitably.引自第20页
Serre to Grothendieck, 1986 Somewhere, you describe your approach to mathematics, in which one does not attack a problem head-on, but one envelopes and dissolves it in a rising tide of general theories. Very good: this is your way of working, and what you have done proves that it does indeed work. For topological vector spaces or algebraic geometry, at least... It is not so clear for number the...
2012-09-13 11:26
Serre to Grothendieck, 1986
Somewhere, you describe your approach to mathematics, in which one does not attack a problem head-on, but one envelopes and dissolves it in a rising tide of general theories. Very good: this is your way of working, and what you have done proves that it does indeed work. For topological vector spaces or algebraic geometry, at least... It is not so clear for number theory (in which the structures involved are far from obvious---or rather, in which all possible structures are involved); I have the same reservation for the theory of modular forms, which is visibly richer than its simple "Lie groups" aspect or its "algebraic geometry---moduli schemes" aspect. Whence this question: did you not come, in fact, around 1968-1970, to realize that the "rising tide" method was powerless against this type of question, and that a different style would be necessary--- which you did not like? 引自第250页
Grothendieck on the military service: I do not think that the danger of losing one's life is such, at this point, that it has become more important than the loss of two years of training (for any young person, scientist or otherwise), leaving aside entirely the moral question (to which most people are apparently indifferent). The minimal probability of being killed does not seem to me to make a...
2012-09-12 19:33
Grothendieck on the military service:
I do not think that the danger of losing one's life is such, at this point, that it has become more important than the loss of two years of training (for any young person, scientist or otherwise), leaving aside entirely the moral question (to which most people are apparently indifferent). The minimal probability of being killed does not seem to me to make a big difference. On the other hand, if certain Academics brought the effects of military service (and, by implication, of the Algerian war) on the scientific level of the country to the attention of the public and the authorities, and required some reforms, it would not exclude the possibility of classical scholars, technicians, firemen and lamp-lighters grouping together to require analogous reforms for themselves, on analogous and to my mind equally valid grounds. Any action in this direction, even if very limited, will contribute to making people realize the consequences of the militarization of the country, and might create a precedent for analogous and vaster actions.
引自第128页
i am trying to learn things, but there is so much to look at and it is so slow. Cartier seems to be an amazing person, especially his speed of understanding, and the incredible amount of things he reads and grasps; I really have the impression that in a few years he will be where you are now. I am exploiting him most profitably.
1 有用 阅微草堂 2016-05-07
局部有方程和坐标，而整体没有方程。研究代数几何，依据代数，不要被几何所误导。Grothendieck的风格不看方程，直接从整体（嵌入）开始-从导出函子开始用同调代数表示一切： "Mittag-Leffler"逼近过程lim作为导出函子, Cartan's theorems A and B （szyzygytic resolutions）作为其特例,
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匆匆浏览了一遍...
1 有用 黑華 2019-05-22
Grothendieck和Serre珍贵书信集，可以看到Grothendieck是怎么发展他的理论的，以及一些非数学的讨论。
1 有用 黑華 2019-05-22
Grothendieck和Serre珍贵书信集，可以看到Grothendieck是怎么发展他的理论的，以及一些非数学的讨论。
1 有用 阅微草堂 2016-05-07
局部有方程和坐标，而整体没有方程。研究代数几何，依据代数，不要被几何所误导。Grothendieck的风格不看方程，直接从整体（嵌入）开始-从导出函子开始用同调代数表示一切： "Mittag-Leffler"逼近过程lim作为导出函子, Cartan's theorems A and B （szyzygytic resolutions）作为其特例,
0 有用 Welfare 2015-01-15
T:QA 29 .G697 A4 2004
0 有用 郦十久 2012-03-04
匆匆浏览了一遍...