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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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 $s=1$.

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

First available in Project Euclid: 18 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

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


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.

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