The -adic monodromy group of abelian varieties over global function fields of characteristic
Ambrus PálDepartment of Mathematics, 180 Queen's Gate, Imperial College, London, SW7 2AZ, United Kingdom
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. 1509–1579DOI 10.4171/DM/903