title: From Frobenius Structures to Differential Equations
creator: Matzat, B. Heinrich
subject: 510
subject: 510 Mathematics
description: Frobenius structures are omnipresent in arithmetic geometry. In this note we show  that over suitable rings, Frobenius endomorphisms define differential structures and  vice versa. This includes, for example, differential rings in positive characteristic  and complete non-archimedean differential rings in characteristic zero. Further,  in the global case, the existence of sufficiently many Frobenius rings is related to  algebraicity properties. These results apply, for example, to t-motives as well as to  p-adic and arithmetic differential equations. 
date: 2008
type: Preprint
type: info:eu-repo/semantics/preprint
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/8075/1/Frobenius2.pdf
identifier: DOI:10.11588/heidok.00008075
identifier: urn:nbn:de:bsz:16-opus-80750
identifier:   Matzat, B. Heinrich  (2008) From Frobenius Structures to Differential Equations.  [Preprint]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/8075/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng