Convolution structures and arithmetic cohomology
| dc.creator | Borisov, Alexandr | |
| dc.date | 1998-07-27 | |
| dc.date | 2001-01-03 | |
| dc.date.accessioned | 2026-07-07T05:25:32Z | |
| dc.date.available | 2026-07-07T05:25:32Z | |
| dc.description | 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 $H^0(L)$ and $H^1(L)$ as some convolution of measures structures. The $H^1$ 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/9807151 | |
| dc.identifier | http://arxiv.org/abs/math/9807151 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77212 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Convolution structures and arithmetic cohomology | |
| dc.type | text |