1998/07/27 by Alexandr Borisov, Borisov, Alexandr · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.math/9807151
Extra section on harmonic analysis included to make the paper more accessible for arithmetic geometers. Also, the ghost-spaces of second kind are treated somewhat differently
openalex publication_date 1998/07/27 · arxiv created 2001/01/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we construct arithmetic analogs of the Riemann-Roch theorem and Serre's duality for line bundles. This improves on the works of Tate and van der Geer - Schoof. We define H0(L) and H1(L) as some convolution of measures structures. The H1 is defined by a procedure very similar to the usual Cech cohomology. We get Serre's duality as Pontryagin duality of convolution structures. We get separately Riemann-Roch formula and Serre's duality. Instead of using the Poisson summation formula, we basically reprove it. The whole theory is pretty much parallel to the geometric case.