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Brauer group

A computation a day: the Brauer group of a number ring

In this post we compute the group \mathrm{Br}(\mathcal{O}_K) where K is a number field.

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Posted in A Computation a Day, Algebraic Geometry, Class field theory, Etale Cohomology, Number Theory and tagged Brauer group, brauer group example, brauer group of a number ring, Brauer group of scheme, class field theory, etale cohomology, number theory on July 20, 2015 by alexyoucis. 6 Comments

The Tate Conjecture over finite fields

In this post we will describe the Tate conjecture for varieties over finite fields, focusing on its various forms, and talking about some applications.

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Posted in Algebraic Geometry, Etale Cohomology, Number Theory and tagged Birch and Swinnerton-Dyer Conjecture, Brauer group, Brauer group of scheme, Hodge conjecture, Intuition, Tate conjecture, Tate conjecture over finite fields on February 28, 2015 by alexyoucis. 5 Comments

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