2025/04/23 by Fernando Peña Vázquez, Vázquez, Fernando Peña
Mathematics · #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2504.16707
openalex publication_date 2025/04/23 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
We introduce a formalism of Hochschild (co)-homology for D-cap modules on smooth rigid analytic spaces based on the homological tools of Ind-Banach D-cap modules. We introduce several categories of D-cap bimodules for which this theory is well-behaved. Among these, the most important example is the category of diagonal C-complexes. We give an explicit calculation of the Hochschild complex for diagonal C-complexes, and show that the Hochschild complex of D-cap is canonically isomorphic to the de Rham complex of X. In particular, we obtain a Hodge-de Rham spectral sequence converging to the Hochschild cohomology groups of D-cap. We obtain explicit formulas relating the Hochschild cohomology and homology of a given diagonal C-complex.