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Creators/Authors contains: "Frei, Sarah"

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  1. ; (, Research in Number Theory)
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  2. ; ; ; ; (, Algebraic Geometry)
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  3. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract Given a smooth projective variety over a number field and an elementof its Brauer group, we consider the specialization of the Brauerclass at a place of good reduction for the variety and the class. Weare interested in the case of K3 surfaces.We show that a Brauer class on a very general polarized K3 surfaceover a number field becomes trivial after specialization at a set ofplaces of positive natural density. We deduce that there exist cubic fourfolds over number fields that are conjecturally irrational, with rational reduction at a positive proportion of places. We also deduce that there are twisted derivedequivalent K3 surfaces which become derived equivalent after reductionat a positive proportion of places. 
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  4. ; ; ; (, Compositio Mathematica)
    null (Ed.)
    We give the first examples of derived equivalences between varieties defined over non-closed fields where one has a rational point and the other does not. We begin with torsors over Jacobians of curves over $$\mathbb {Q}$$ and $$\mathbb {F}_q(t)$$ , and conclude with a pair of hyperkähler 4-folds over $$\mathbb {Q}$$ . The latter is independently interesting as a new example of a transcendental Brauer–Manin obstruction to the Hasse principle. The source code for the various computations is supplied as supplementary material with the online version of this article. 
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