Abstract: The Brauer group of a variety can detect both algebraic and arithmetic properties of the underlying object. In particular, the Brauer-Manin obstruction that lies in the Brauer group can obstruct the existence of rational points. In this talk, I will discuss an algorithm to compute the prime torsion of the Brauer group of an elliptic curve E explicitly over various ground fields k. This algorithm gives generators and relations of the torsion subgroup as tensor products of symbol algebras over the function field of the elliptic curve. As a consequence of the algorithm, I will give an upper bound on the symbol length of the prime torsion of Br(E)/Br(k).
Link to paper: [ Ссылка ]
Subject codes: 16K50, 14H52, 14F22
Email: cu9da@virginia.edu
Website: [ Ссылка ]
