Geometric aspects of Dwork theory / edited by Alan Adolphson ... [et al.].

Format:

Book

Contributor:

Adolphson, Alan, 1951-

Series:

De Gruyter Proceedings in Mathematics

Language:

English

Subjects (All):

Geometry, Algebraic.

Number theory.

p-adic analysis.

Physical Description:

1 online resource (568 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; New York : W. de Gruyter, 2004.

Language Note:

English

Summary:

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 thep-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

Contents:

Geometric Aspects of Dwork Theory. Volume I

Front matter

Table of Contents of Volume I

The Mathematical Publications of Bernard Dwork

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

Exponential sums and free hyperplane arrangements

Sur la conjecture des p-courbures de Grothendieck-Katz et un problème de Dwork

Hilbert modular varieties of low dimension

On Dwork cohomology for singular hypersurfaces

On Dwork cohomology and algebraic D-modules

An introduction to the theory of p-adic representations

Smooth p-adic analytic spaces are locally contractible. II

Germs of analytic varieties in algebraic varieties: canonical metrics and arithmetic algebraization theorems

Thirty years later

Approximation of eigenforms of infinite slope by eigenforms of finite slope

Crystalline cohomology of singular varieties

Stacks of twisted modules and integral transforms

On some rational generating series occuring in arithmetic geometry

Compactifications arithmétiques des variétés de Hilbert et formes modulaires de Hilbert pour Γ1(c, n)

Geometric Aspects of Dwork Theory. Volume II

Fr -ont matter Table of Contents of Volume II

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

Introduction to p-adic q-difference equations (weak Frobenius structure and transfer theorems)

An introduction to the Riemann-Hilbert correspondence for unit F-crystals

Introduction to L-functions of F-isocrystals

Notes on some t-structures

Non-vanishing modulo p of Hecke L-values

On semistable reduction and the calculation of nearby cycles

Inequalities related to Lefschetz pencils and integrals of Chern classes

Full faithfulness for overconvergent F-isocrystals

Frobenius action, F-isocrystals and slope filtration

Conjecture on Abbes-Saito filtration and Christol-Mebkhout filtration

Transformation de Fourier des D-modules arithmétiques I

Boyarsky principle for D-modules and Loeser's conjecture

Cohomological descent in rigid cohomology

Monodromie locale et fonctions Zêta des log schémas

Trace et dualité relative pour les D-modules arithmétiques

Geometric moment zeta functions

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786612194382

9781282194380

1282194380

9783110198133

3110198134

OCLC:

232160505