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SUMMARY:Sean Howe (University of Utah)
DTSTART:20200625T160000Z
DTEND:20200625T172000Z
DTSTAMP:20260423T052545Z
UID:RAMpAGe/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/2/">
 A p-adic transcendence criterion for CM Galois representations</a>\nby Sea
 n Howe (University of Utah) as part of Recent Advances in Modern p-Adic Ge
 ometry (RAMpAGe)\n\n\nAbstract\nWe show that a crystalline Galois represen
 tation with rational de Rham lattice admits a slope filtration with abelia
 n isoclinic subquotients. As a corollary\, we find that a $p$-divisible gr
 oup over $\\mathcal{O}_{\\mathbb{C_p}}$ has complex multiplication if and 
 only if it can be defined over a complete discretely valued subfield and i
 ts Hodge-Tate filtration is algebraic -- this is a $p$-adic analog of clas
 sical 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 on
 e paw as those with algebraic Hodge-Tate and de Rham periods. The correspo
 nding archimedean transcendence results for Shimura varieties fit into a b
 roader framework of bialgebraicity that plays an important role in the And
 re-Oort conjecture\, and\, time permitting\, we discuss some ideas of what
  this might look like in the $p$-adic setting.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/2/
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