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

  • Ambrus Pál

    Department of Mathematics, 180 Queen's Gate, Imperial College, London, SW7 2AZ, United Kingdom
The $p$-adic monodromy group of abelian varieties over global function fields of characteristic $p$ cover
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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 . 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 -adic Tate modules, for different from . We also show such a result for general compatible systems incorporating overconvergent -isocrystals, conditional on a result of Abe.

Cite this article

Ambrus Pál, The -adic monodromy group of abelian varieties over global function fields of characteristic . Doc. Math. 27 (2022), pp. 1509–1579

DOI 10.4171/DM/903