6 papers
On the torsion in the cohomology of the integral structure sheaf of affinoid adic spaces
Emiliano Torti
We prove that the cohomology of the integral structure sheaf of a normal affinoid adic space over a non-archimedean field of characteristic zero is uniformly torsion. This result o…
Lagrange's theorem for a family of finite flat group schemes over local Artin rings
Emiliano Torti
Let R be a local Artin ring with residue field k of positive characteristic. We prove that every finite flat group scheme over R whose special fiber belongs to a certain explicit f…
Lattices in rigid analytic representations
Andrea Conti, Emiliano Torti
For a profinite group and a rigid analytic space , we study when an -linear representation of admits a lattice, i.e. an $\mathcal O_{\mathcal X(\mat…
On the existence of analytic families of G-stable lattices and their reductions
Emiliano Torti
In this article, we prove the existence of rigid analytic families of -stable lattices with locally constant reductions inside families of representations of a topologically com…
Local constancy for reductions of two-dimensional crystalline representations
Emiliano Torti
We prove the existence of local constancy phenomena for reductions in a general prime power setting of two-dimensional irreducible crystalline representations. Up to twist, these r…
On the level raising of cuspidal eigenforms modulo prime powers
Emiliano Torti
In this article we prove level raising for cuspidal eigenforms modulo prime powers (for odd primes) of weight and arbitrary character, extending the result in weight two…