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Birational Geometry, Rational Curves, and Arithmetic pp 205–227Cite as

On the Ubiquity of Twisted Sheaves

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Abstract

We describe some recent work on the uses of twisted sheaves in algebra, arithmetic, and geometry. In particular, we touch on the role of twisted sheaves in:

  1. 1.

    The geometry of the period-index problem for the Brauer group

  2. 2.

    The connection between finiteness of the u-invariant and Colliot-Thélène’s conjecture on 0-cycles

  3. 3.

    The link between the Tate conjecture for K3 surfaces and finiteness of the set of isomorphism classes of K3 surfaces over a finite field

  4. 4.

    The geometry of rational curves on the moduli spaces of supersingular K3 surfaces

Mathematics Subject Classification codes (2000): 14F22, 14H10, 11E81

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Acknowledgements

During the writing of this paper, the author was partially supported by a Sloan Fellowship and NSF CAREER grant DMS-1056129. He thanks the referee for helpful comments and the Simons Foundation for its generous support of the Simons Symposia.

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  1. Department of Mathematics, University of Washington, Seattle, WA, USA

    Max Lieblich

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  1. Max Lieblich
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Correspondence to Max Lieblich .

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Editors and Affiliations

  1. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Fedor Bogomolov

  2. , Department of Mathematics, Rice University, S. Main St. 6100, Houston, 77251-1892, Texas, USA

    Brendan Hassett

  3. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Yuri Tschinkel

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Lieblich, M. (2013). On the Ubiquity of Twisted Sheaves. In: Bogomolov, F., Hassett, B., Tschinkel, Y. (eds) Birational Geometry, Rational Curves, and Arithmetic. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6482-2_10

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