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University of Sydney Algebra Seminar

Angus McAndrew

Friday 5 May, 12-1pm, Place: Carslaw 173

A descent theorem for K3 surfaces

Descent problems have fascinated mathematicians since ancient times. A modern descent question asks for the field of definition of a given algebraic variety, i.e. whether there is a criterion for when it can be descended from a field to a smaller one. A theorem of Grothendieck gives an answer to this question in the case of abelian varieties and transcendental field extensions. We will discuss a general conjecture inspired by this, and prove it in the case of K3 surfaces, under some hypotheses. The proof uses Madapusi-Pera's work on the Kuga-Satake construction.