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6 votes
1 answer
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Binomial coefficients in discrete valuation rings

Let $V$ be a complete discrete valuation ring whose residue field is a finite field $k=\mathbf{F}_q$. Let $\pi\in V$ be a uniformizer. For any integer $d,n\ge 0$, define: $${\pi^d \choose n} := \...
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3 votes
0 answers
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Discrete vs. finitely generated subgroups of the adèles

If $U\subseteq\mathbf{R}^n$ is an additive subgroup, discrete with respect to the induced topology, then $U$ is a finitely generated abelian group. Question. Given a discrete additive subgroup $U\...
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1 vote
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152 views

Image of pullback for Brauer groups

If a have a dominant morphism $\pi:X \rightarrow \mathbb{P}^{1}$ where $X$ is a projective, geometrically integral $k$-scheme. Then this gives rise to a pullback map \begin{align*} \pi^{*}:\text{Br}(k(...
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