A p-adic transcendence criterion for CM Galois representations
Sean Howe (University of Utah)
Abstract: We show that a crystalline Galois representation with rational de Rham lattice admits a slope filtration with abelian isoclinic subquotients. As a corollary, we find that a $p$-divisible group over $\mathcal{O}_{\mathbb{C_p}}$ has complex multiplication if and only if it can be defined over a complete discretely valued subfield and its Hodge-Tate filtration is algebraic -- this is a $p$-adic analog of classical transcendence results for complex abelian varieties due to Schneider, Cohen, and Shiga-Wolfart. More generally, we characterize the special points of the diamond moduli of mixed-characteristic local shtuka with one paw as those with algebraic Hodge-Tate and de Rham periods. The corresponding archimedean transcendence results for Shimura varieties fit into a broader framework of bialgebraicity that plays an important role in the Andre-Oort conjecture, and, time permitting, we discuss some ideas of what this might look like in the $p$-adic setting.
commutative algebraalgebraic geometrynumber theory
Audience: researchers in the topic
Recent Advances in Modern p-Adic Geometry (RAMpAGe)
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Organizers: | David Hansen*, Arthur-César Le Bras*, Jared Weinstein* |
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