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6
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111 views

What is the etale cohomology of a product?

Let $X$ be a (smooth, projective if you wish) variety over a field $k$. I'm mostly interested in $k=\mathbb{F}_q$. What can one say about the etale cohomology ring $H_{et}^*(X \times_k X)$, say for ...
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0answers
179 views

Mayer-Vietoris on Fibered Products

Suppose $M \xrightarrow{p} X$ is a surjective submersion of smooth manifolds. Define the fibered product in this case: $$M \times_X M = \{ (m_1, m_2) \in M \times M | p(m_1) = p(m_2) \}$$ and let $U =...
0
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141 views

Fiber products of adic spaces

In the notes from Peter Scholze's class at Berkeley he makes the following remark: "Let us call a Huber pair $(A, A^+)$ admissible if $A$ is finitely generated over a ring of definition $A_0 \subset A^...