2025/04/23 by Vázquez, Fernando Peña
#14G2 (Primary) 81R60 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2504.16689
Let X be a smooth rigid space with an action of a finite group G satisfying that X/G is represented by a rigid space. We construct sheaves of p-adic Cherednik algebras on the small étale site of the quotient X/G, and study some of their properties. The sheaves of p-adic Cherednik algebras are sheaves of Fréchet K-algebras on X/G, which can be regarded as p-adic analytic versions of the sheaves of Cherednik algebras associated to the action of a finite group on a smooth algebraic variety defined by P. Etingof. Furthermore, their sections on small enough G-invariant affinoid spaces are canonically Fréchet-Stein algebras. Along the way, we construct sheaves of infinite order twisted differential operators on X, we give a G-equivariant classification of the Atiyah algebras (Picard algebroids) on X, and study the category of co-admissible modules over a sheaf of infinite order twisted differential operators.