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Let G be a connected split reductive group over a complete discrete valuation ring of mixed characteristic. We use the theory of intermediate extensions due to Abe-Caro and arithmetic Beilinson-Bernstein localization to classify irreducible modules over the crystalline distribution algebra of G in terms of overconvergent isocrystals on locally closed subspaces in the (formal) flag variety of G. We treat the case of SL(2) as an example.
The main result of the paper is a flat extension theorem for positive linear functionals on *-algebras. The theorem is applied to truncated moment problems on cylinder sets, on matrices of polynomials and on enveloping algebras of Lie algebras.
The crystalline period map is a tool for linearizing $p$-divisible groups. It has been applied to study the Langlands correspondences, and has possible applications to the homotopy groups of spheres. The original construction of the period map is inh
We introduce the notions of infinitesimal extension and square-zero extension in the context of simplicial commutatie algebras. We next investigate their mutual relationship and we show that the Postnikov tower of a simplicial commutative algebra is
We consider stacks of filtered phi-modules over rigid analytic spaces and adic spaces. We show that these modules parametrize p-adic Galois representations of the absolute Galois group of a p-adic field with varying coefficients over an open substack
Given three arbitrary vector bundles on the Fargues-Fontaine curve where one of them is assumed to be semistable, we give an explicit and complete criterion in terms of Harder-Narasimha polygons on whether there exists a short exact sequence among th