Brauer-Siegel theorem for elliptic surfaces

TL;DR

This paper extends the classical Brauer-Siegel theorem to higher-dimensional cases, specifically for constant families of elliptic curves and abelian varieties over global function fields, providing new theoretical insights.

Contribution

It introduces a higher-dimensional analogue of the Brauer-Siegel theorem for elliptic surfaces and abelian varieties over global function fields.

Findings

Proves an analogue of the Brauer-Siegel theorem for constant families of elliptic curves.

Establishes theoretical results for abelian varieties over global function fields.

Abstract

We consider higher-dimensional analogues of the classical Brauer-Siegel theorem focusing on the case of abelian varieties over global function fields. We prove such an analogue in the case of constant families of elliptic curves and abelian varieties.