BOUNDS ON THE TAMAGAWA NUMBERS OF A CRYSTALLINE REPRESENTATION OVER TOWERS OF CYCLOTOMIC EXTENSIONS

Antonio Lei

doi:10.2748/tmj/1512183627

Tohoku Mathematical Journal, Second Series

Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735

BOUNDS ON THE TAMAGAWA NUMBERS OF A CRYSTALLINE REPRESENTATION OVER TOWERS OF CYCLOTOMIC EXTENSIONS

Antonio Lei

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Keywords: Tamagawa numbers, cyclotomic extensions, $p$-adic representations, $p$-adic Hodge theory, Wach modules, modular forms

JOURNAL FREE ACCESS

2017 Volume 69 Issue 4 Pages 497-524

DOI https://doi.org/10.2748/tmj/1512183627

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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.

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