Pierre Colmez's Books

Grothendieck-Serre Correspondence

By: Alexandre Grothendieck,Pierre Colmez

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Grothendieck-Serre Correspondence

By: Alexandre Grothendieck,Pierre Colmez

The letters presented in the book were mainly written between 1955 and 1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. The reader can follow the creation of some of the most important notions of modern mathematics, like sheaf cohomology, schernes, Riemann-Roch type theorems, algebraic fundamental group, motives. The letters also reflect the mathematical and political atmosphere of this period (Bourbaki, Paris, Harvard, Princeton, war in Algeria, etc.) Also included are a few letters written between 1984 and 1987. The letters are supplemented by J.-P. Serre's notes, which give explanations, corrections, and references further results." "The book should be useful to specialists in algebraic geometry, in history of mathematics, and to all mathematicians who want to understand how great mathematics is created."--BOOK JACKET.

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602

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082183424X

ISBN 13

9780821834244

Cocycles de groupe pour $mathrm {GL}_n$ et arrangements d?hyperplans

By: Nicolas Bergeron,Pierre Charollois,Luis E. Garc¡a

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Cocycles de groupe pour $mathrm {GL}_n$ et arrangements d?hyperplans

By: Nicolas Bergeron,Pierre Charollois,Luis E. Garc¡a

Ce livre constitue un expos‚ d‚taill‚ de la s‚rie de cours donn‚s en 2020 par le Prof. Nicolas Bergeron, titulaire de la Chaire Aisenstadt au CRM de Montr‚al. L'objet de ce texte est une ample g‚n‚ralisation d'une famille d'identit‚s classiques, notamment la formule d'addition de la fonction cotangente ou celle des s‚ries d'Eisenstein. Le livre relie ces identit‚s … la cohomologie de certains sous-groupes arithm‚tiques du groupe lin‚aire g‚n‚ral. Il rend explicite ces relations au moyen de la th‚orie des symboles modulaires de rang sup‚rieur, d‚voilant finalement un lien concret entre des objets de nature topologique et alg‚brique. This book provides a detailed exposition of the material presented in a series of lectures given in 2020 by Prof. Nicolas Bergeron while he held the Aisenstadt Chair at the CRM in Montr‚al. The topic is a broad generalization of certain classical identities such as the addition formulas for the cotangent function and for Eisenstein series. The book relates these identities to the cohomology of arithmetic subgroups of the general linear group. It shows that the relations can be made explicit using the theory of higher rank modular symbols, ultimately unveiling a concrete link between topological and algebraic objects. I think that the text ?Cocycles de groupe pour $mathrm{GL}_n$ et arrangements d'hyperplans? is terrific. I like how it begins in a leisurely, enticing way with an elementary example that neatly gets to the topic. The construction of these ?meromorphic function?-valued modular symbols are fundamental objects, and play (and will continue to play) an important role. ?Barry Mazur, Harvard University

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146

Publisher

American Mathematical Society, Centre de Recherches Math‚matiques

Published Date

ISBN 10

1470474115

ISBN 13

9781470474119

Lectures on N_X(p)

By: Jean-Pierre Serre

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Lectures on N_X(p)

By: Jean-Pierre Serre

Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic cohomology and group representations, presented in

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Page Count

169

Publisher

CRC Press

Published Date

ISBN 10

1466501936

ISBN 13

9781466501935

Categories and Sheaves

By: Masaki Kashiwara,Pierre Schapira

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Categories and Sheaves

By: Masaki Kashiwara,Pierre Schapira

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

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Page Count

496

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540279504

ISBN 13

9783540279501

Renormalization and Galois Theories

By: Frédéric Fauvet,Jean-Pierre Ramis

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Renormalization and Galois Theories

By: Frédéric Fauvet,Jean-Pierre Ramis

This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics.

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284

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190736

ISBN 13

9783037190739

Homo Academicus

By: Pierre Bourdieu

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Homo Academicus

By: Pierre Bourdieu

In this highly original work, Pierre Bourdieu turns his attention to the academic world of which he is part and offers a brilliant analysis of modern intellectual culture. The academy is shown to be not just a realm of dialogue and debate, but also a sphere of power in which reputations and careers are made, defended and destroyed. Employing the distinctive methods for which he has become well known, Bourdieu examines the social background and practical activities of his fellow academics--from Foucault, Derrida, and Lacan to figures who are lesser known but not necessarily less influential. Bourdieu analyzes their social origins and current positions, how much they publish and where they publish it, their institutional connections, media appearances, political involvements and so on. This enables Bourdieu to construct a map of the intellectual field in France and to analyze the forms of capital and power, the lines of conflict and the patterns of change, which characterize the system of higher education in France today. Homo Academicus paints a vivid and dynamic picture of French intellectual life today and develops a general approach to the study of modern culture and education. It will be of great interest to students of sociology, education and politics as well as to anyone concerned with the role of intellectuals and higher education today.

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374

Publisher

Stanford University Press

Published Date

ISBN 10

0804717982

ISBN 13

9780804717984

Oeuvres - Collected Papers IV

1985 - 1998

By: Jean-Pierre Serre

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Oeuvres - Collected Papers IV

1985 - 1998

By: Jean-Pierre Serre

The impact and influence of J.-P. Serre ́s work have been notable ever since his doctoral thesis on homotopy groups. The abundance of findings and deep insights found in his research and survey papers ranging from topology, several complex variables, and algebraic geometry to number theory, group theory, commutative algebra and modular forms, continues to provide inspiring reading for mathematicians working in these areas, in their research and their teaching. Characteristic of Serre ́s publications are the many open questions he formulates pointing to further directions for research. In four volumes of Collected Papers he has provided comments on and corrections to most articles, and described the current status of the open questions with reference to later findings. In this softcover edition of volume IV, two recently published articles have been added, one on the life and works of André Weil, the other one on Finite Subgroups of Lie Groups. From the reviews: "This is the fourth volume of J-P. Serre's Collected Papers covering the period 1985-1998. Items, numbered 133-173, contain "the essence'' of his work from that period and are devoted to number theory, algebraic geometry, and group theory. Half of them are articles and another half are summaries of his courses in those years and letters. Most courses have never been previously published, nor proofs of the announced results. The letters reproduced, however (in particular to K. Ribet and M.-F. Vignéras), provide indications of some of those proofs. Also included is an interview with J-P. Serre from 1986, revealing his views on mathematics (with the stress upon its integrity) and his own mathematical activity. The volume ends with Notes which complete the text by reporting recent progress and occasionally correct it. Zentralblatt MATH

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Page Count

710

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540435654

ISBN 13

9783540435655

Grothendieck-Serre Correspondence

By: Alexandre Grothendieck,Pierre Colmez

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Grothendieck-Serre Correspondence

By: Alexandre Grothendieck,Pierre Colmez

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Solve jigsaw puzzle

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Page Count

602

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082183424X

ISBN 13

9780821834244

Book's by Pierre Colmez

Grothendieck-Serre Correspondence

Grothendieck-Serre Correspondence

Cocycles de groupe pour $mathrm {GL}_n$ et arrangements d?hyperplans

Cocycles de groupe pour $mathrm {GL}_n$ et arrangements d?hyperplans

Lectures on N_X(p)

Lectures on N_X(p)

Categories and Sheaves

Categories and Sheaves

Renormalization and Galois Theories

Renormalization and Galois Theories

Homo Academicus

Homo Academicus

Oeuvres - Collected Papers IV

Oeuvres - Collected Papers IV

Grothendieck-Serre Correspondence

Grothendieck-Serre Correspondence

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