We formulate a few conjectures on some hypothetical coherent sheaves on the stacks of
arithmetic local Langlands parameters, including their roles played in the local-global …

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 construct projective varieties in mixed characteristic whose singularities model, in
generic cases, those of tamely potentially crystalline Galois deformation rings for unramified …

We show that framed deformation rings of mod p representations of the absolute Galois
group of a p-adic local field are complete intersections of expected dimension. We …

Let X be a smooth p-adic formal scheme over OK with adic generic fibre X. We obtain a
global equivalence between the category Vect.. X/¡; xO¡ Œ 1 p/of rational Hodge–Tate …

Caraiani was supported in part by NSF grant DMS-1501064, by a Royal Society University
Research Fellowship, and by ERC Starting Grant 804176. Emerton was supported in part by …

FORMAL ALGEBRAIC STACKS Contents 1. Introduction 1 2. 2-categorical background 4 3.
Stack-theoretic background 18 4. Ind-algebra Page 1 FORMAL ALGEBRAIC STACKS …

We give criteria for certain morphisms from an algebraic stack to a (not necessarily
algebraic) stack to admit an (appropriately defined) scheme-theoretic image. We apply our …

Let K/Q p be unramified. Inside the Emerton–Gee stack X 2, one can consider the locus of
two-dimensional mod 𝑝 representations of Gal⁢(K ̄/K) having a crystalline lift with specified …

We study the weight part of Serre's conjecture for generic n-dimensional mod p Galois
representations. We first generalize Herzig's conjecture to the case where the field is …