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A Computation a Day

A computation a day: a pullback pushforward

In this post we compute the Galois representation $i^\ast R^m j_\ast\mathbb{Q}_\ell$ where $j:\mathbb{G}_{m,\overline{k}}\hookrightarrow\mathbb{A}^1_k$ is the natural inclusion and $i:\text{Spec}(k)\hookrightarrow \mathbb{A}^1_k$ is the inclusion of the origin.

Posted in A Computation a Day, Algebraic Geometry, Etale Cohomology, Topology and tagged Algebraic Geometry, étale fundamental group, etale cohomology, examples, Intuition, motivation, strict henselization on September 19, 2016 by alexyoucis. 1 Comment

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.

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. 1 Comment

A computation a day: compactly supported cohomology

In this post we compute the compactly supported cohomology of some simple varieties.

Posted in A Computation a Day, Algebraic Geometry, Etale Cohomology and tagged compactly supported cohomology, curves, etale cohomology, example on March 27, 2015 by alexyoucis. 2 Comments

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