Severi-Brauer varieties of semidirect product algebras

Details Severi-Brauer varieties of semidirect product algebras Severi-Brauer varieties of semidirect product algebras

2002-06-15

arxiv.org/abs/math/0206154v1

Mathematics

Rings and Algebras

22 pages

Scientific paper

A conjecture of Amitsur states that two Severi-Brauer varieties are birationally isomorphic if and only if the underlying algebras are the same degree and generate the same cyclic subgroup of the Brauer group. It is known that generating the same cyclic subgroup is a necessary condition, however it has not yet been shown to be sufficient. In this paper we examine the case where the algebras have a maximal subfield $K/F$ of degree $n$ with Galois closure $E/F$ whose Galois group is of the form $C_n \rtimes H$, where $E^H = K$ and $|H|$ is prime to $n$. For such as we show that the conjecture is true for certain cases of $n$ and $H$. In particular we prove the conjecture in the case that $G$ is a dihedral group of order $2p$, where $p$ is prime

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