Cohomology of adéle class groups of algebraic tori

Saikat Biswas

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arXiv · 1508.04711

Cohomology of adéle class groups of algebraic tori

Saikat Biswas

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Abstract

Let $T$ be an algebraic torus defined over a global field $K$ and split over a finite cyclic extension. In this paper, we determine the Herbrand quotient of the adéle class group of $T$. Our result can be seen as an extension of the so-called first inequality of global class field theory.

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Saikat Biswas. 2015-12-15. Cohomology of adéle class groups of algebraic tori. https://arxiv.org/abs/1508.04711

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