Convolution Structures and Arithmetic Cohomology

Alexandr Borisov

doi:10.1023/A:1023297625434

Convolution Structures and Arithmetic Cohomology

Alexandr Borisov

Mathematics and Statistics

Binghamton University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Convolution structures are group-like objects that were extensively studied by harmonic analysts. We use them to define H⁰ and H ¹ for Arakelov divisors over number fields. We prove the analogs of the Riemann-Roch and Serre duality theorems. This brings more structure to the works of Tate and van der Geer and Schoof. The H¹ is defined by a procedure very similar to the usual Ĉech cohomology. Serre's duality becomes Pontryagin duality of convolution structures. The whole theory is parallel to the geometric case.

Original language	English
Pages (from-to)	237-254
Number of pages	18
Journal	Compositio Mathematica
Volume	136
Issue number	3
DOIs	https://doi.org/10.1023/A:1023297625434
State	Published - May 2003

Keywords

Arakelov divisors
Convolution structures
Number fields
Pontryagin duality
Riemann-Roch
Serre's duality

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KW - Arakelov divisors

KW - Convolution structures

KW - Number fields

KW - Pontryagin duality

KW - Riemann-Roch

KW - Serre's duality

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Convolution Structures and Arithmetic Cohomology

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Keywords

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