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000806775 0247_ $$a10.1007/978-3-319-49763-1$$2doi
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000806775 24500 $$aGeometry over nonclosed fields /$$cFedor Bogomolov, Brendan Hassett, Yuri Tschinkel, editors.
000806775 264_1 $$aCham, Switzerland :$$bSpringer,$$c2017.
000806775 300__ $$a1 online resource.
000806775 336__ $$atext$$btxt$$2rdacontent
000806775 337__ $$acomputer$$bc$$2rdamedia
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000806775 4901_ $$aSimons Symposia,$$x2365-9564
000806775 5050_ $$6880-01$$aPreface; Contents; On the Kobayashi Pseudometric, Complex Automorphisms and Hyperkähler Manifolds; 1 Introduction; 2 Preliminaries; 3 (Royden -- )Kobayashi Pseudometric on Abelian Fibrations; 4 Automorphisms of Infinite Order; 5 Metric Geometry of Kobayashi Quotients; 6 Eigenvalues and Periodic Points of Hyperbolic Automorphisms; References; Lines on Cubic Hypersurfaces Over Finite Fields; 1 Introduction; 2 Definitions and Tools; 2.1 The Weil and Tate Conjectures; 2.2 The Katz Trace Formula; 2.3 The Galkin -- Shinder Formulas; 2.4 Abelian Varieties Over Finite Fields; 3 Cubic Surfaces.
000806775 5058_ $$a4 Cubic Threefolds4.1 The Zeta Function of the Surface of Lines; 4.2 Existence of Lines on Smooth Cubic Threefolds Over Large Finite Fields; 4.3 Computing Techniques: The Bombieri -- Swinnerton-Dyer Method; 4.4 Lines on Mildly Singular Cubic Threefolds; 4.5 Examples of Cubic Threefolds; 4.6 Average Number of Lines; 5 Cubic Fourfolds; 5.1 The Zeta Function of the Fourfold of Lines; 5.2 Existence of Lines over Large Finite Fields; 5.3 Existence of Lines over Some Finite Fields; 5.4 Examples of Cubic Fourfolds; 6 Cubics of Dimensions 5 or More; References.
000806775 5058_ $$aPerverse Sheaves of Categories and Non-rationality1 Introduction; 2 Perverse Sheaves of Categories; 2.1 Definitions; 2.2 Some More Examples; 3 Deformations of Perverse Sheaves of Categories and Poisson Deformations; 3.1 Warmup: Deformations of mathbbP2; 3.2 Noncommutative Deformations of mathbbP3; 3.3 Perverse Sheaves of Categories and Elliptic Curves; 4 Landau -- Ginzburg Model Computations for Threefolds; 4.1 The LG Model of a Quartic Double Solid; 4.2 Torsion in Cohomology of the LG Model; 4.3 The Cubic Threefold; 4.4 The Quartic Double Fourfold; 4.5 Base Change and Torsion.
000806775 5058_ $$a1.2 Morphisms to Brauer -- Severi Varieties.
000806775 506__ $$aAccess limited to authorized users.
000806775 520__ $$aBased on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.
000806775 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed February 20, 2017).
000806775 650_0 $$aGeometry, Algebraic.
000806775 650_0 $$aAlgebraic fields.
000806775 7001_ $$aBogomolov, Fedor,$$eeditor.
000806775 7001_ $$aHassett, Brendan,$$eeditor.
000806775 7001_ $$aTschinkel, Yuri,$$eeditor.
000806775 77608 $$iPrint version:$$tGeometry over nonclosed fields.$$dCham, Switzerland : Springer, 2017$$z3319497626$$z9783319497624$$w(OCoLC)961004925
000806775 830_0 $$aSimons Symposia.
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