Affiliation:
1. Department of Mathematics, Oberlin College, 10 North Professor Street, Oberlin, OH 44074, USA
Abstract
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.
Funder
National Science Foundation
Division of Mathematical Sciences
RNMS: Geometric Structures and Representation Varieties
Publisher
Oxford University Press (OUP)
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