LCA(2), Weil index, and product formula

TL;DR

This paper explores the category LCA(2) of non-locally compact abelian topological groups, extends the Weil index concept, and applies these to derive product formulas for curves over local fields and arithmetic surfaces.

Contribution

It introduces an extension of the Weil index within the category LCA(2) and applies it to arithmetic geometry problems.

Findings

Derived product formulas for curves over local fields

Extended Weil index concept to LCA(2) groups

Connected topological group theory with arithmetic geometry

Abstract

In this paper we study the category LCA(2) of certain non-locally compact abelian topological groups, and extend the notion of Weil index. As applications we deduce some product formulas for curves over local fields and arithmetic surfaces.