Geometric Aspects of Dwork Theory (eBook)
1129 Seiten
De Gruyter (Verlag)
978-3-11-019813-3 (ISBN)
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 written by leading experts in the field. The book willprovide an indispensable resource for all those wishing to approach the frontiers of research in arithmetic algebraic geometry.
Frontmatter 1
Table of Contents of Volume I 7
The Mathematical Publications of Bernard Dwork 11
Exponential sums and generalized hypergeometric functions. I: Cohomology spaces and Frobenius action 15
Exponential sums and free hyperplane arrangements 57
Sur la conjecture des p-courbures de Grothendieck–Katz et un problème de Dwork 69
Hilbert modular varieties of low dimension 127
On Dwork cohomology for singular hypersurfaces 191
On Dwork cohomology and algebraic D-modules 259
An introduction to the theory of p-adic representations 269
Smooth p-adic analytic spaces are locally contractible. II 307
Germs of analytic varieties in algebraic varieties: canonical metrics and arithmetic algebraization theorems 385
Thirty years later 433
Approximation of eigenforms of infinite slope by eigenforms of finite slope 451
Crystalline cohomology of singular varieties 465
Stacks of twisted modules and integral transforms 477
On some rational generating series occuring in arithmetic geometry 523
Compactifications arithmétiques des variétés de Hilbert et formes modulaires de Hilbert pour G1(c, n) 541
Frontmatter 569
Table of Contents of Volume II 573
Variétés et formes modulaires de Hilbert arithmétiques pour 1(c, n) 575
Introduction to p-adic q-difference equations (weak Frobenius structure and transfer theorems) 635
An introduction to the Riemann–Hilbert correspondence for unit F-crystals 697
Introduction to L-functions of F-isocrystals 721
Notes on some t-structures 731
Non-vanishing modulo p of Hecke L-values 755
On semistable reduction and the calculation of nearby cycles 805
Inequalities related to Lefschetz pencils and integrals of Chern classes 825
Full faithfulness for overconvergent F-isocrystals 839
Frobenius action, F-isocrystals and slope filtration 857
Conjecture on Abbes–Saito filtration and Christol–Mebkhout filtration 865
Transformation de Fourier des D-modules arithmétiques I 877
Boyarsky principle for D-modules and Loeser’s conjecture 929
Cohomological descent in rigid cohomology 951
Monodromie locale et fonctions Zêta des log schémas 1003
Trace et dualité relative pour les D-modules arithmétiques 1059
Geometric moment zeta functions 1133
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"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