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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.AG2024

Almost Coherence of Higher Direct Images

Tongmu He

For a flat proper morphism of finite presentation between schemes with almost coherent structural sheaves (in the sense of Faltings), we prove that the higher direct images of quas…