Tohoku Mathematical Journal
2017
December
SECOND SERIES VOL. 69, NO. 4

Tohoku Math. J.
69 (2017), 497-524

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

Author Antonio Lei

(Received January 28, 2015, revised October 2, 2015)
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.

Mathematics Subject Classification. Primary 11F80; Secondary, 11R18, 11F11, 11F85, 11R23.
Key words and phrases. Tamagawa numbers, cyclotomic extensions, $p$-adic representations, $p$-adic Hodge theory, Wach modules, modular forms.

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