3 papers
math.AG2025
Perfectoidness via Sen Theory and Applications to Shimura Varieties
Tongmu He
Sen's theorem on the ramification of a -adic analytic Galois extension of -adic local fields shows that its perfectoidness is equivalent to the non-vanishing of its arithmeti…
math.AG2025
The -adic Galois Cohomology of Valuation Fields
Tongmu He
We compute the Galois cohomology of any -adic valuation field extension of a pre-perfectoid field. Moreover, we obtain a generalization and also a new proof of the classical res…
math.NT2025
Characterizing perfectoid covers of abelian varieties
Rebecca Bellovin, Hanlin Cai, Sean Howe +1
We give a simple characterization of all perfectoid profinite étale covers of abelian varieties in terms of the Hodge-Tate filtration on the -adic Tate module. We also compute…