Brauer equivalent number fields and the geometry of quaternionic Shimura varieties

Abstract

Two number fields are said to be Brauer equivalent if there is an isomorphism between their Brauer groups that commutes with restriction. In this paper, we prove a variety of number theoretic results about Brauer equivalent number fields (for example, they must have the same signature). These results are then applied to the geometry of certain arithmetic locally symmetric spaces. As an example, we construct incommensurable arithmetic locally symmetric spaces containing exactly the same set of proper immersed totally geodesic surfaces.

Publisher

Oxford University Press

Publication Date

6-1-2019

Publication Title

Quarterly Journal of Mathematics

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.1093/qmath/hay061

Keywords

Commensurability

Language

English

Format

text

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