Tohoku Mathematical Journal

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

Antonio Lei

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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.

Article information

Tohoku Math. J. (2), Volume 69, Number 4 (2017), 497-524.

First available in Project Euclid: 2 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F80: Galois representations
Secondary: 11R18: Cyclotomic extensions 11F11: Holomorphic modular forms of integral weight 11F85: $p$-adic theory, local fields [See also 14G20, 22E50] 11R23: Iwasawa theory

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


Lei, Antonio. Bounds on the Tamagawa numbers of a crystalline representation over towers of cyclotomic extensions. Tohoku Math. J. (2) 69 (2017), no. 4, 497--524. doi:10.2748/tmj/1512183627.

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