Higher solutions of hypergeometric systems and Dwork cohomology
type: Item
instance of: scholarly article
title: Higher solutions of hypergeometric systems and Dwork cohomology
zbMATH Open document ID: 0931.14012
author: Alan Adolphson
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2000-03-08T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108483
review text: Some new results on hypergeometric functions and rings generated by monomials are given. First, a resolution of the hypergeometric differential module \(M_a\) (associated to the \(N\)-variable Weyl algebra) is constructed. This enables to obtain higher formal and analytic solutions of \(M_a\). Then, a connection between these solutions and the algebraic Dwork cohomology (of de Rham-type) is established. By standard results in the theory of \(D\)-modules, it is proven that the Dwork cohomology is finite dimensional.
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 14F10
zbMATH DE Number: 1319601
zbMATH Keywords: \(D\)-modules
zbMATH Keywords: hypergeometric functions
zbMATH Keywords: monomials
zbMATH Keywords: hypergeometric differential module
zbMATH Keywords: Dwork cohomology
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
cites work: Hypergeometric functions and rings generated by monomials
cites work: Exponential sums and Newton polyhedra: cohomology and estimates
cites work: The analytic continuation of generalized functions with respect to a parameter
cites work: Q3784384
cites work: On the zeta function of a hypersurface. I
cites work: Q4280723
cites work: Q5590963
cites work: Hypergeometric functions and toric varieties
cites work: Polyedres de Newton et nombres de Milnor
cites work: Finiteness of De Rham Cohomology
cites work: Q5585729
cites work: Q5522742
description: scientific article; zbMATH DE number 1319601