Tohoku Mathematical Journal

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

Antonio Lei

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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.

Article information

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

Dates
First available in Project Euclid: 2 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1512183627

Digital Object Identifier
doi:10.2748/tmj/1512183627

Mathematical Reviews number (MathSciNet)
MR3732885

Zentralblatt MATH identifier
06850811

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.tmj/1512183627


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References

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