arXiv subjects

Guillem Tarrach

Publications and source records attributed to Guillem Tarrach.

2 recordsLinked to original sources

arXiv2023

$S$-arithmetic (co)homology and $p$-adic automorphic forms

We study the $S$-arithmetic (co)homology of reductive groups over number fields with coefficients in (duals of) certain locally algebraic and locally analytic representations for finite sets of primes $S$. We use our results to construct eigenvarieties associated to parabolic subgroups at places in $S$ and certain classes of supercuspidal and algebraic representations of their Levi factors. We show that these agree with eigenvarieties constructed using overconvergent homology and that for definite unitary groups they are closely related to the Bernstein eigenvarieties constructed by Breuil-Ding.

math.NT↗

arXiv2023

The $p$-arithmetic homology of mod $p$ representations of $\mathrm{GL}_2(\mathbb{Q}_p)$

We compute the non-Eisenstein systems of Hecke eigenvalues contributing to the $p$-arithmetic homology of irreducible smooth mod $p$ representations $π$ of $\mathrm{GL}_2(\mathbb{Q}_p)$ and to the cohomology of their duals. We show that in most cases they are associated to odd irreducible 2-dimensional Galois representations whose local component at $p$ corresponds under the mod $p$ local Langlands correspondence to a smooth representation that contains $π$ as a subrepresentation.

math.NT↗