Trees
Trees

Author: Jean-Pierre Serre

Publisher: Springer Science & Business Media

Published: 2002-11-25

Total Pages: 168

ISBN-13: 9783540442370

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The seminal ideas of this book played a key role in the development of group theory since the 70s. Several generations of mathematicians learned geometric ideas in group theory from this book. In it, the author proves the fundamental theorem for the special cases of free groups and tree products before dealing with the proof of the general case. This new edition is ideal for graduate students and researchers in algebra, geometry and topology.

The Governesses
The Governesses

Author: Anne Serre

Publisher: New Directions Publishing

Published: 2018-10-30

Total Pages: 76

ISBN-13: 0811228088

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Publishers Weekly Best Books in Fiction 2018 The sensational US debut of a major French writer—an intense, delicious meringue of a novella In a large country house shut off from the world by a gated garden, three young governesses responsible for the education of a group of little boys are preparing a party. The governesses, however, seem to spend more time running around in a state of frenzied desire than attending to the children’s education. One of their main activities is lying in wait for any passing stranger, and then throwing themselves on him like drunken Maenads. The rest of the time they drift about in a kind of sated, melancholy calm, spied upon by an old man in the house opposite, who watches their goings-on through a telescope. As they hang paper lanterns and prepare for the ball in their own honor, and in honor of the little boys rolling hoops on the lawn, much is mysterious: one reviewer wrote of the book’s “deceptively simple words and phrasing, the transparency of which works like a mirror reflecting back on the reader.” Written with the elegance of old French fables, the dark sensuality of Djuna Barnes and the subtle comedy of Robert Walser, this semi-deranged erotic fairy tale introduces American readers to the marvelous Anne Serre.

Local Algebra
Local Algebra

Author: Jean-Pierre Serre

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 139

ISBN-13: 3662042037

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This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.

The Beginners
The Beginners

Author: Anne Serre

Publisher: New Directions Publishing

Published: 2021-07-05

Total Pages: 122

ISBN-13: 0811230325

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Quintessential Anne Serre—this restless, prowling novel explores love as a form of greed, and confused need as one shape of bereftness Anna has been living happily for twenty years with loving, sturdy, outgoing Guillaume when she suddenly (truly at first sight) falls in love with Thomas. Intelligent and handsome, but apparently scarred by a terrible early emotional wound, he reminds Anna of Jude the Obscure. Adrift and lovelorn, she tries unsuccessfully to fend off her attraction, torn between the two men. “How strange it is to leave someone you love for someone you love. You cross a footbridge that has no name, that’s not named in any poem. No, nowhere is a name given to this bridge, and that is why Anna found it so difficult to cross.” Anne Serre offers here, in her third book in English, her most direct novel to date. The Beginners is unpredictable, sensual, exhilarating, oddly moral, perverse, absurd—and unforgettable.

Serre's Conjecture
Serre's Conjecture

Author: T.Y. Lam

Publisher: Springer

Published: 2006-11-15

Total Pages: 240

ISBN-13: 3540359265

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From the Preface: "I felt it would be useful for graduate students to see a detailed account of the sequence of mathematical developments which was inspired by the Conjecture, and which ultimately led to its full solution.... I offered a course on Serre's Conjecture to a small group of graduate students in January, 1977 [at the University of California, Berkeley] one year after its solution by Quillen and Suslin. My course was taught very much in the spirit of a mathematical 'guided tour'. Volunteering as the guide, I took upon myself the task of charting a route through all the beautiful mathematics surrounding the main problem to be treated; the 'guide' then leads his audience through the route, on to the destination, pointing out the beautiful sceneries and historical landmarks along the way."

A Course in Arithmetic
A Course in Arithmetic

Author: J-P. Serre

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 126

ISBN-13: 1468498843

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This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.-J. Sansuc (Chapters I-IV) and J.-P. Ramis and G. Ruget (Chapters VI-VII). They were very useful to me; I extend here my gratitude to their authors.

Local Fields
Local Fields

Author: Jean-Pierre Serre

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 249

ISBN-13: 1475756739

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The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.

Galois Cohomology
Galois Cohomology

Author: Jean-Pierre Serre

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 215

ISBN-13: 3642591418

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This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.