arXiv:2210.01404v2 [math.NT] 1 Feb 2023 Page 1 An introduction to the categorical p-adic
Langlands program Matthew Emerton, Toby Gee, and Eugen Hellmann Abstract. We give an …

We study the locally analytic vectors in the completed cohomology of modular curves and
determine the eigenvectors of a rational Borel subalgebra of. As applications, we prove a …

We prove new cases of Fontaine-Mazur conjecture on two-dimensional Galois
representations over $\mathbb {Q} $ when the residual representation is reducible. Our …

Under an assumption on the existence of p-adic Galois representations, we carry out Taylor–
Wiles patching (in the derived category) for the completed homology of the locally symmetric …

We associate infinitesimal characters to (twisted) families of $ L $-parameters and $ C $-
parameters of $ p $-adic reductive groups. We use the construction to study the action of the …

Let p be a prime number and K a finite extension of Q p. We state conjectures on the smooth
representations of GL n (K) that occur in spaces of mod p automorphic forms (for compact …

For a finite extension F of, Drinfeld defined a tower of coverings of (the Drinfeld half-plane).
For, we describe a decomposition of the p-adic geometric étale cohomology of this tower …

Let G be a split connected reductive algebraic group over Q p such that both G and its dual
group G ˆ have connected centers. Motivated by a hypothetical p-adic Langlands …

We compute p-adic étale and pro-étale cohomologies of Drinfeld half-spaces. In the pro-
étale case, the main input is a comparison theorem for p-adic Stein spaces; the cohomology …

Motivated by the Langlands program in representation theory, number theory, and geometry,
the theory of representations of a reductive p-adic group, originally in complex vector …