Geometric Aspects of Dwork Theory
Description
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 / Votes
"The proceedings will be useful for a wide range of readers interested in modern applications of p-adic methods."(spor) in: EMS-Newsletter 9/2007More details
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Content
Frontmatter
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 G1(c, n)
Geometric Aspects of Dwork Theory. Volume II
Frontmatter
Table of Contents of Volume II
Variétés et formes modulaires de Hilbert arithmétiques pour G1(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
