Bounds on the Tamagawa numbers of a crystalline representation over towers of cyclotomic extensions

TL;DR

This paper investigates bounds on Tamagawa numbers for crystalline representations over cyclotomic extension towers, improving previous asymptotic bounds under specific conditions.

Contribution

It provides new bounds on Tamagawa numbers for crystalline representations, refining earlier asymptotic estimates in particular cases.

Findings

Improved asymptotic bounds on Tamagawa numbers

Conditions under which bounds are tightened

Application to specific crystalline representations

Abstract

In this paper, we study the Tamagawa numbers of a crystalline representation over a tower of cyclotomic extensions under certain technical conditions on the representation. In particular, we show that we may improve the asymptotic bounds given in the thesis of Arthur Laurent in certain cases.