## Arithmetic Geometry and Number Theory RTG Seminar: F-isocrystals with logarithmic decay, slope filtrations, and monodromy

Seminar | April 22 | 3-5 p.m. | 748 Evans Hall

Joe Kramer Miller, UC Irvine

Department of Mathematics

Wan conjectured that the variation of zeta functions along towers of curves associated to the $p$-adic etale cohomology of a fibration of smooth proper ordinary varieties should satisfy several stabilizing properties. The most basic of these conjectures state that the genera of the curves in these towers grow in a regular way. We state and prove a generalization of this conjecture, which applies to the graded pieces of the slope filtration of an overconvergent $F$-isocrystal.

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