Prime torsion in the Brauer group of an elliptic curve
The Brauer group is an invariant in algebraic geometry and number theory, that can be associated to a field, variety, or scheme. Let k be a field of characteristic different from 2 or 3, and let E be an elliptic curve over k. The Brauer group of E is a torsion abelian group with elements given by Morita equivalence classes of central simple algebras over the function field k(E). The MerkurjevSuslin theorem implies that any such element can be described by a tensor product of symbol algebras. We give a description of elements in the dtorsion of the Brauer group of E in terms of these tensor products, provided that the dtorsion of E is krational and k contains a primitive dth root of unity. Furthermore, if d = q is a prime, we give an algorithm to compute the qtorsion of the Brauer group over any field k of characteristic different from 2,3, and q containing a primitive qth root of unity.
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Electronic Theses & Dissertations
 Copyright Status
 Attribution 4.0 International
 Material Type

Theses
 Authors

Ure, Charlotte
 Thesis Advisors

Kulkarni, Rajesh S.
 Committee Members

Levin, Aaron D.
Pappas, Georgios
Shapiro, Michael
Rapinchuk, Igor
 Date
 2019
 Subjects

Torsion
Brauer groups
Curves, Elliptic
 Program of Study

Mathematics  Doctor of Philosophy
 Degree Level

Doctoral
 Language

English
 Pages
 viii, 89 pages
 ISBN

9781392227565
1392227569
 Permalink
 https://doi.org/doi:10.25335/2vvc2v29