Monday, February 11, 2019
Algebra and Geometry Seminar
Ramification of $p$-adic etale sheaves coming from ordinary
Joe Kramer-Miller, Department of Mathematics, UC Irvine
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.