Arithmetic theory of q-difference equations: The q-analogue of Grothendieck-Katz’s conjecture on p-curvatures

Grothendieck's conjecture on p-curvatures predicts that an arithmetic differential equation has a full set of algebraic solutions if and only if its reduction in positive characteristic has a full set of rational solutions for almost all finite places. It is equivalent to Katz's conjectura...

Full description

Saved in:
Bibliographic Details
Published in:Inventiones mathematicae 2002-12, Vol.150 (3), p.517-578
Main Author: Di Vizio, Lucia
Format: Article
Language:English
Subjects:
Mathematics
Number Theory
Quantum Algebra
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Grothendieck's conjecture on p-curvatures predicts that an arithmetic differential equation has a full set of algebraic solutions if and only if its reduction in positive characteristic has a full set of rational solutions for almost all finite places. It is equivalent to Katz's conjectural description of the generic Galois group. In this paper we prove an analogous statement for arithmetic q-difference equation.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-002-0241-z