Thursday, October 24, 2024
2:30 PM -
3:45 PM
Linde Hall 187
Algebra and Geometry Seminar
$p$-adic monodromy and mod $p$ unlikely intersections
Ruofan Jiang,
Department of Mathematics,
UC Berkeley,
We introduce a mod $p$ analogue of the Mumford—Tate conjecture, which governs the $p$-adic monodromy of families of mod $p$ abelian varieties. It turns out that the conjecture is closely related to a notion of formal linearity on the moduli space of abelian varieties. Surprisingly, the conjecture can be reduced to an unlikely intersection problem of Ax—Schanuel type, a phenomenon that is unique to positive characteristic. This gives rise to new perspectives for attacking the Mumford—Tate problem, say, algebraization and p-adic O-minimal theory...
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