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Thursday 29 Sep 2016The p-adic monodromy group of abelian varieties over global function fields of characteristic p

Ambrus Pal - Imperial College

H103 14:30-16:30

We prove an analogue of the Tate isogeny conjecture and the semi-simplicity conjecture for overconvergent crystalline Dieudonne modules of abelian varieties defined over global function fields of characteristic p. As a corollary we deduce that monodromy groups of such overconvergent crystalline Dieudonne 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.

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