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- W2927963574 abstract "For a $p$-adic curve $X$, we study conditions under which all classes in the $n$-torsion of $Br(X)$ are $mathbb{Z}/n$-cyclic. We show that in general not all classes are $mathbb{Z}/n$-cyclic classes. On the other hand, if $X$ has good reduction and $n$ is prime to $p$, of if $X$ is an elliptic curve over $mathbb{Q}_p$ with split multiplicative reduction and $n$ is a power of $p$, then we prove that all order $n$ elements of $Br(X)$ are $mathbb{Z}/n$-cyclic. Finally, if $X$ has good reduction and its function field $K(X)$ contains all $p^2$-th roots of $1$, we show the existence of indecomposable division algebras over $K(X)$ with period $p^2$ and index $p^3$." @default.
- W2927963574 created "2019-04-11" @default.
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- W2927963574 date "2018-02-07" @default.
- W2927963574 modified "2023-09-27" @default.
- W2927963574 title "Cyclicity and indecomposability in the Brauer group of a $p$-adic curve" @default.
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