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

• Pubblicazione: Berlin ; ; New York, : W. de Gruyter, 2004
• Descrizione fisica: 1 online resource (568 p.)
• Disciplina: 516.3/5
• Soggetto topico: Geometry, Algebraic; Number theory; p-adic analysis
• Altri autori: AdolphsonAlan <1951->
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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
• Sommario/riassunto: 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
• Titolo autorizzato: Geometric aspects of Dwork theory
• ISBN: 1-282-19438-0; 9786612194382; 3-11-019813-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910784289003321
• Lo trovi qui: Univ. Federico II
• Serie: De Gruyter Proceedings in Mathematics