Abstract Let X→ Y be a fibration whose fibers are complete intersections of r quadrics. We
develop new categorical and algebraic tools—a theory of relative homological projective …

This is a survey of the geometry of complex cubic fourfolds with a view toward rationality
questions. Topics include classical constructions of rational examples, Hodge structures and …

We discuss some aspects of the behavior of specialization at a finite place of Néron–Severi
groups of K3 surfaces over number fields. We give optimal lower bounds for the Picard …

We isolate a class of smooth rational cubic fourfolds X containing a plane whose associated
quadric surface bundle does not have a rational section. This is equivalent to the nontriviality …

We report on progress in the qualitative study of rational points on rationally connected
varieties over number fields, also examining integral points, zero-cycles, and non-rationally …

We prove that the Fano variety of lines of a generic cubic fourfold containing a plane is
isomorphic to a moduli space of twisted stable complexes on a K3 surface. On the other …

Let X be a proper smooth algebraic variety defined over a number field k. We denote by Ωk
the set of all the places of k, and by kv the completion of k with respect to v∈ Ωk. Let Br (X) …

We prove that in a family of projective threefolds defined over an algebraically closed field,
the locus of rational fibers is a countable union of closed subsets of the locus of separably …

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Rational Points on K3 Surfaces and Derived Equivalence Page 1 Rational Points on K3
Surfaces and Derived Equivalence Brendan Hassett and Yuri Tschinkel Abstract. We study K3 …