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Gerasimos Dousmanis

Publications and source records attributed to Gerasimos Dousmanis.

5 recordsLinked to original sources
arXiv2013

A note on reductions of 2-dimensional crystalline Galois representations

Let $p$ be an odd prime number, $K_{f}$ the finite unramified extension of $\mathbb{Q}_{p}$ of degree $f$, and $G_{K_{f}}$ its absolute Galois group. We construct analytic families of étale $(φ,Γ)$-modules which give rise to some families of 2-dimensional crystalline representations of $G_{K_{f}}$ with length of filtration $\geq p$. As an application, we prove that the modulo $p$ reductions of the members of each such family (with respect to appropriately chosen Galois-stable lattices) are constant.

math.NT↗
arXiv2010

On reductions of families of crystalline Galois representations

Let K_{f} be the finite unramified extension of Q_{p} of degree f and E any finite large enough coefficient field containing K_{f}. We construct analytic families of étale (Phi,Gamma)-modules which give rise to families of crystalline E-representations of the absolute Galois group G_{K_{f}} of K_{f}. For any irreducible effective two-dimensional crystalline E-representation of G_{K_{f}} with labeled Hodge-Tate weights {0,-k_{i}}_{τ_{i}} induced from a crystalline character of G_{K_{2f}}, we construct an infinite family of crystalline E-representations of G_{K_{f}} of the same Hodge-Tate type which contains it. As an application, we compute the semisimplified mod p reductions of the members of each such family.

math.NT↗
arXiv2009

Rank two filtered $(ϕ, N)$-modules with Galois descent data and coefficients

Let $K$ be any finite extension of $Q_{p}$, $L$ any finite Galois extension of $K$ and $E$ any finite large enough coefficient field containing $L$. We classify two-dimensional, F-semistable $E$-representations of $G_{K}$, by listing the isomorphism classes of rank two weakly admissible filtered $(ϕ,N,L/K,E)$-modules.

math.NT↗