Titlebook: Brauer Groups and Obstruction Problems; Moduli Spaces and Ar Asher Auel,Brendan Hassett,Bianca Viray Book 2017 Springer International Publi

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Rational Points on K3 Surfaces and Derived Equivalence,We study K3 surfaces over non-closed fields and relate the notion of derived equivalence to arithmetic problems.

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,Arithmetically Cohen–Macaulay Bundles on Cubic Fourfolds Containing a Plane,We study ACM bundles on cubic fourfolds containing a plane exploiting the geometry of the associated quadric fibration and Kuznetsov’s treatment of their bounded derived categories of coherent sheaves. More precisely, we recover the K3 surface naturally associated to the fourfold as a moduli space of Gieseker stable ACM bundles of rank four.

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On a Local-Global Principle for ,, of Function Fields of Surfaces over a Finite Field,Let . be the function field of a smooth projective surface . over a finite field .. In this article, following the work of Parimala and Suresh, we establish a local-global principle for the divisibility of elements in . by elements in ..

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Cohomology and the Brauer Group of Double Covers,We calculate the 2-torsion subgroup of the Brauer group of a ramified double covering of a rational surface over an algebraically closed field. This and more general results are obtained by working with cohomology with mod 2 coefficients. Applications to the Brauer groups of K3 surfaces are discussed.

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0743-1643 Obus..· Ekin Ozman..· Raman Parimala..· Alexander Perry..· Alena Pirutka..· Justin Sawon..· Alexei N. Skorobogatov..· Paolo Stellari.· Sho Tanimoto..· Hugh Thomas..· Yuri Tschinkel..· Anthony Várilly-Alvarado.978-3-319-83601-0978-3-319-46852-5Series ISSN 0743-1643 Series E-ISSN 2296-505X

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Book 2017endan Hassett..· Colin Ingalls.· Martí Lahoz..· Emanuele Macrì..· Kelly McKinnie..· Andrew Obus..· Ekin Ozman..· Raman Parimala..· Alexander Perry..· Alena Pirutka..· Justin Sawon..· Alexei N. Skorobogatov..· Paolo Stellari.· Sho Tanimoto..· Hugh Thomas..· Yuri Tschinkel..· Anthony Várilly-Alvarado.

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Komponenten im Magnetlagersystem,s arising from symmetric resolutions of line bundles on . to yield Azumaya represen- tatives for the 2-torsion Brauer classes on .. We show that when . is in our base field, both constructions give the same result.

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