Linkage of Sets of Cyclic Algebras

Adam Chapman

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arXiv · 2104.08349

Linkage of Sets of Cyclic Algebras

Adam Chapman

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Abstract

Let $p$ be a prime integer and $F$ the function field in two algebraically independent variables over a smaller field $F_0$. We prove that if $\operatorname{char}(F_0)=p\geq 3$ then there exist $p^2-1$ cyclic algebras of degree $p$ over $F$ that have no maximal subfield in common, and if $\operatorname{char}(F_0)=0$ then there exist $p^2$ cyclic algebras of degree $p$ over $F$ that have no maximal subfield in common.

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Adam Chapman. 2021-04-16. Linkage of Sets of Cyclic Algebras. https://arxiv.org/abs/2104.08349

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