Locally Equivalent Correspondences
Group Theory
2018-11-14 v2 Geometric Topology
Number Theory
Rings and Algebras
Abstract
Given a pair of number fields with isomorphic rings of adeles, we construct bijections between objects associated to the pair. For instance we construct an isomorphism of Brauer groups that commutes with restriction. We additionally construct bijections between central simple algebras, maximal orders, various Galois cohomology sets, and commensurability classes of arithmetic lattices in simple, inner algebraic groups. We show that under certain conditions, lattices corresponding to one another under our bijections have the same covolume and pro-congruence completion. We also make effective a finiteness result of Prasad and Rapinchuk.
Cite
@article{arxiv.1505.04755,
title = {Locally Equivalent Correspondences},
author = {Benjamin Linowitz and D. B. McReynolds and Nicholas Miller},
journal= {arXiv preprint arXiv:1505.04755},
year = {2018}
}
Comments
Final Version. To appear in Ann. Inst. Fourier