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On the Ubiquity of Twisted Sheaves

In: Birational Geometry, Rational Curves, and Arithmetic

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  • Max Lieblich

    (University of Washington, Department of Mathematics)

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. The geometry of the period-index problem for the Brauer group 2. The connection between finiteness of the u-invariant and Colliot-Thélène’s conjecture on 0-cycles 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. The geometry of rational curves on the moduli spaces of supersingular K3 surfaces

Suggested Citation

  • Max Lieblich, 2013. "On the Ubiquity of Twisted Sheaves," Springer Books, in: Fedor Bogomolov & Brendan Hassett & Yuri Tschinkel (ed.), Birational Geometry, Rational Curves, and Arithmetic, edition 127, pages 205-227, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-6482-2_10
    DOI: 10.1007/978-1-4614-6482-2_10
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