2 citations · 7 across the 9 of their papers we have counts for
9 papers
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…
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 t…
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…
Purity for Perfectoidness
Tongmu He
There has been a long-standing question about whether being perfectoid for an algebra is local in the analytic topology. We provide affirmative answers for the algebras (e.g., over…
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…
Sen Operators and Lie Algebras arising from Galois Representations over -adic Varieties
Tongmu He
Any finite-dimensional -adic representation of the absolute Galois group of a -adic local field with imperfect residue field is characterized by its arithmetic and geometric…
Cohomological Descent for Faltings' -adic Hodge Theory and Applications
Tongmu He
Faltings' approach in -adic Hodge theory can be schematically divided into two main steps: firstly, a local reduction of the computation of the -adic étale cohomology of a sm…
Faltings extension and Hodge-Tate filtration for abelian varieties over -adic local fields with imperfect residue fields
Tongmu He
Let be a complete discrete valuation field of characteristic with not necessarily perfect residue field of characteristic . We define a Faltings extension of $\mathcal…
Topological Conjugacy of Non-hyperbolic Linear Flows
Tongmu He
The topological equivalence classification for linear flows on had been completely solved by Kuiper and independently Ladis in 1973. However, Ladis' proof was publis…