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book: Geometric Aspects of Dwork Theory
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Geometric Aspects of Dwork Theory

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Languages: English, French
Published/Copyright: 2004
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De Gruyter Proceedings in Mathematics
This book is in the series
De Gruyter Proceedings in Mathematics

About this book

This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998).

It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on the geometric applications of the p-adic analytic techniques originating in Dwork's work, their connection to various recent cohomology theories and to modular forms.

The two volumes contain both important new research and illuminating survey articles written by leading experts in the field. The book will provide an indispensable resource for all those wishing to approach the frontiers of research in arithmetic algebraic geometry.

Reviews

"The proceedings will be useful for a wide range of readers interested in modern applications of p-adic methods."
(spor) in: EMS-Newsletter 9/2007

Topics

  • Geometric Aspects of Dwork Theory. Volume I
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    Frontmatter

    i
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    Table of Contents of Volume I

    vii
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    The Mathematical Publications of Bernard Dwork

    xi
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    Exponential sums and generalized hypergeometric functions. I: Cohomology spaces and Frobenius action

    1
    Alan Adolphson
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    Exponential sums and free hyperplane arrangements

    43
    Alan Adolphson and Steven Sperber
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    Sur la conjecture des p-courbures de Grothendieck–Katz et un problème de Dwork

    55
    Yves André
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    Hilbert modular varieties of low dimension

    113
    Fabrizio Andreatta and Eyal Z. Goren
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    On Dwork cohomology for singular hypersurfaces

    177
    Francesco Baldassarri and Pierre Berthelot
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    On Dwork cohomology and algebraic D-modules

    245
    Francesco Baldassarri and Andrea D’Agnolo
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    An introduction to the theory of p-adic representations

    255
    Laurent Berger
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    Smooth p-adic analytic spaces are locally contractible. II

    293
    Vladimir G. Berkovich
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    Germs of analytic varieties in algebraic varieties: canonical metrics and arithmetic algebraization theorems

    371
    Jean-Benoît Bost
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    Thirty years later

    419
    Gilles Christol
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    Approximation of eigenforms of infinite slope by eigenforms of finite slope

    437
    Robert F. Coleman and William A. Stein
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    Crystalline cohomology of singular varieties

    451
    Richard Crew
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    Stacks of twisted modules and integral transforms

    463
    Andrea D’Agnolo and Pietro Polesello
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    On some rational generating series occuring in arithmetic geometry

    509
    Jan Denef and François Loeser
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    Compactifications arithmétiques des variétés de Hilbert et formes modulaires de Hilbert pour Γ1(c, n)

    527
    Mladen Dimitrov
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  • Geometric Aspects of Dwork Theory. Volume II
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    Frontmatter

    i
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    Table of Contents of Volume II

    v
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    Variétés et formes modulaires de Hilbert arithmétiques pour Γ1(c, n)

    555
    Mladen Dimitrov and Jacques Tilouine
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    Introduction to p-adic q-difference equations (weak Frobenius structure and transfer theorems)

    615
    Lucia Vizio
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    An introduction to the Riemann–Hilbert correspondence for unit F-crystals

    677
    Matthew Emerton and Mark Kisin
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    Introduction to L-functions of F-isocrystals

    701
    Jean-Yves Etesse
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    Notes on some t-structures

    711
    Ofer Gabber
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    Non-vanishing modulo p of Hecke L-values

    735
    Haruzo Hida
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    On semistable reduction and the calculation of nearby cycles

    785
    Luc Illusie
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    Inequalities related to Lefschetz pencils and integrals of Chern classes

    805
    Nicholas M. Katz and Rahul Pandharipande
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    Full faithfulness for overconvergent F-isocrystals

    819
    Kiran S. Kedlaya
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    Frobenius action, F-isocrystals and slope filtration

    837
    Bernard Stum
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    Conjecture on Abbes–Saito filtration and Christol–Mebkhout filtration

    845
    Shigeki Matsuda
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    Transformation de Fourier des D-modules arithmétiques I

    857
    Christine Noot-Huyghe
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    Boyarsky principle for D-modules and Loeser’s conjecture

    909
    Tomohide Terasoma
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    Cohomological descent in rigid cohomology

    931
    Nobuo Tsuzuki
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    Monodromie locale et fonctions Zêta des log schémas

    983
    Isabelle Vidal
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    Trace et dualité relative pour les D-modules arithmétiques

    1039
    Anne Virrion
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    Geometric moment zeta functions

    1113
    Daqing Wan
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
August 22, 2008
eBook ISBN:
9783110198133
Hardcover published on:
August 25, 2004
Hardcover ISBN:
9783110174786
Pages and Images/Illustrations in book
Main content:
1129
https://doi.org/10.1515/9783110198133
eBook ISBN: 9783110198133
Hardcover ISBN: 9783110174786
Keywords for this book
Algebraische Geometrie; D-Modul; Zetafunktion
Audience(s) for this book
Research Mathematicians; Academic Libraries
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