eprintid: 8075
rev_number: 9
eprint_status: archive
userid: 1
dir: disk0/00/00/80/75
datestamp: 2008-02-06 09:57:47
lastmod: 2015-04-21 16:06:44
status_changed: 2012-08-14 15:24:13
type: preprint
metadata_visibility: show
creators_name: Matzat, B. Heinrich
title: From Frobenius Structures to Differential Equations
ispublished: pub
subjects: 510
divisions: 708000
cterms_swd: Frobenius-Endomorphismus
cterms_swd: Differentialgleichung
cterms_swd: Frobenius-Ring
cterms_swd: Differentialring
abstract: 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. 
abstract_translated_lang: eng
date: 2008
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00008075
portal_cluster_id: p-iwrpp
portal_order: 08075
ppn_swb: 1646175980
own_urn: urn:nbn:de:bsz:16-opus-80750
language: eng
bibsort: MATZATBHEIFROMFROBEN2008
full_text_status: public
series: IWR-Preprints
citation:   Matzat, B. Heinrich  (2008) From Frobenius Structures to Differential Equations.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/8075/1/Frobenius2.pdf