Cocycles de groupe pour GLn et arrangements d’hyperplans
by Nicolas Bergeron, Pierre Charollois and Luis E. García
Description
Note: This book is in French.
Ce livre constitue un exposé détaillé de la série de cours donnés en 2020 par le Prof. Nicolas Bergeron, titulaire de la Chaire Aisenstadt au CRM de Montréal.
L'objet de ce texte est une ample généralisation d'une famille d'identités classiques, notamment la formule d'addition de la fonction cotangente ou celle des séries d'Eisenstein. Le livre relie ces identités à la cohomologie de certains sous-groupes arithmétiques du groupe linéaire général. Il rend explicite ces relations au moyen de la théorie des symboles modulaires de rang supérieur, dévoilant finalement un lien concret entre des objets de nature topologique et algébrique.
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 Montréal.
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.
Graduate students and researchers interested in modular forms and/or special values of L-functions.
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Reviews
I think that the text “Cocycles de groupe pour GLn 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
American Mathematical Society
View all titlesBibliographic Information
- Publisher American Mathematical Society and Centre de Recherches Mathématiques
- Orginal LanguageFrench
- ISBN/Identifier 9781470474119
- Publication Country or regionUnited States
- FormatHardback
- Pages127
- ReadershipProfessional and Scholarly
- Publish StatusPublished
- Copyright Year2023
- SeriesCentre de Recherches Mathématiques Monograph Series
- Series Part39
- Reference CodeCRMM39
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