Representations of Higher Adelic Groups and Arithmetic
A. N. Parshin

TL;DR
This paper explores the structure and harmonic analysis of adelic groups associated with higher-dimensional schemes, focusing on their representations and applications in number theory.
Contribution
It introduces new representations of adelic Heisenberg groups derived from two-dimensional schemes, advancing the understanding of higher adelic groups.
Findings
Developed harmonic analysis tools for adelic groups on two-dimensional schemes
Constructed new representations of adelic Heisenberg groups
Analyzed the structure of n-dimensional local fields
Abstract
We discuss the following topics: n-dimensional local fields and adelic groups; harmonic analysis on local fields and adelic groups for two-dimensional schemes (function spaces, Fourier transform, Poisson formula); representations of discrete Heisenberg groups; adelic Heisenberg groups and their representations arising from two-dimensional schemes.
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Taxonomy
Topicsadvanced mathematical theories · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry
