Journal of the Mathematical Society of Japan

On the Galois structure of arithmetic cohomology II: ray class groups

David BURNS and Asuka KUMON

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Abstract

We investigate the explicit Galois structure of ray class groups. We then derive consequences of our results concerning both the validity of Leopoldt’s Conjecture and the existence of families of explicit congruence relations between the values of Dirichlet $L$-series at $s=1$.

Article information

Source
J. Math. Soc. Japan, Volume 70, Number 2 (2018), 481-517.

Dates
First available in Project Euclid: 18 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1524038665

Digital Object Identifier
doi:10.2969/jmsj/07027321

Mathematical Reviews number (MathSciNet)
MR3787731

Zentralblatt MATH identifier
06902433

Subjects
Primary: 11G35: Varieties over global fields [See also 14G25]
Secondary: 11R33: Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10] 11R34: Galois cohomology [See also 12Gxx, 19A31]

Keywords
ray class groups Galois structure Leopoldt’s Conjecture Dirichlet $L$-series

Citation

BURNS, David; KUMON, Asuka. On the Galois structure of arithmetic cohomology II: ray class groups. J. Math. Soc. Japan 70 (2018), no. 2, 481--517. doi:10.2969/jmsj/07027321. https://projecteuclid.org/euclid.jmsj/1524038665


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