Bryden.Cais

Affiliation: University of Arizona

Title Of Talk: Iwasawa theory of unramified geometric $Z_p$-extensions of function fields

Abstract: In this talk, I will describe a novel Iwasawa theory for unramified $Z_p$-extensions of global function fields over an algebraically closed field of characteristic p. In this context, the p-adic slopes of Frobenius acting on the first crystalline cohomology of the associated $Z_p$-tower of algebraic curves provide a new kind of Iwasawa-theoretic object to study, and I will present evidence for a recent conjecture about the limiting behavior of these slopes.

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