The $p$-adic monodromy group of abelian varieties over global function fields of characteristic $p$

File Description SizeFormat 
1512.03587v1.pdfWorking paper634.69 kBAdobe PDFView/Open
Title: The $p$-adic monodromy group of abelian varieties over global function fields of characteristic $p$
Authors: Pal, A
Item Type: Working Paper
Abstract: We prove an analogue of the Tate isogeny conjecture and the semi-simplicity conjecture for overconvergent crystalline Dieudonné modules of abelian varieties defined over global function fields of characteristic p. As a corollary we deduce that monodromy groups of such overconvergent crystalline Dieudonné modules are reductive, and after a finite base change of coefficients their connected components are the same as the connected components of monodromy groups of Galois representations on the corresponding l-adic Tate modules, for l different from p. We also show such a result for general compatible systems incorporating overconvergent F-isocrystals, conditional on a result of Abe.
Issue Date: 11-Dec-2015
URI: http://hdl.handle.net/10044/1/64429
Publisher: arXiv
Copyright Statement: © 2015 The Author.
Keywords: math.NT
Notes: 56 pages, comments welcome!
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commonsx