Representations of Higher Adelic Groups and Arithmetic

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.