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Event Series:
Algebraic Geometry in String Theory Seminar
Derived categories of genus one curves and torsors over abelian varieties
April 4, 2024 @ 10:30 am - 11:30 am
Algebraic Geometry in String Theory Seminar
Speaker: Jonathan Rosenberg, University of Maryland
Title: Derived categories of genus one curves and torsors over abelian varieties
Abstract: Studying orientifold string theories on elliptic curves or abelian
varieties motivates studying the derived category of coherent sheaves on
a genus one curve or a torsor over an abelian variety over the reals
(as opposed to the complex numbers).
In joint work with Nirnajan Ramachandran (to appear in MRL), we show that
a genus one curve over a perfect field determines a class in the relative
Brauer group of the Jacobian elliptic curve, and that there is a natural
Mukai-type derived equivalence between the original genus one curve
and the Jacobian twisted by the Brauer class. The proof extends to
torsors over abelian varieties (of any dimension).