A Survey Of The Hodge Conjecture
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A Survey of the Hodge Conjecture
Author | : James Dominic Lewis |
Publsiher | : American Mathematical Soc. |
Total Pages | : 386 |
Release | : 1999 |
Genre | : Geometry, Algebraic |
ISBN | : 9780821805688 |
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This book provides an introduction to a topic of central interest in transcendental algebraic geometry: the Hodge conjecture. Consisting of 15 lectures plus addenda and appendices, the volume is based on a series of lectures delivered by Professor Lewis at the Centre de Recherches Mathematiques (CRM). The book is a self-contained presentation, completely devoted to the Hodge conjecture and related topics. It includes many examples, and most results are completely proven or sketched. The motivation behind many of the results and background material is provided. This comprehensive approach to the book gives it a 'user-friendly' style. Readers need not search elsewhere for various results. The book is suitable for use as a text for a topics course in algebraic geometry. It includes an appendix by B. Brent Gordon.
A Survey of the Hodge Conjecture
Author | : James D. Lewis,B. Brent Gordon |
Publsiher | : American Mathematical Soc. |
Total Pages | : 368 |
Release | : 2016-05-06 |
Genre | : Electronic Book |
ISBN | : 9781470428525 |
Download A Survey of the Hodge Conjecture Book in PDF, Epub and Kindle
This book provides an introduction to a topic of central interest in transcendental algebraic geometry: the Hodge conjecture. Consisting of 15 lectures plus addenda and appendices, the volume is based on a series of lectures delivered by Professor Lewis at the Centre de Recherches Mathematiques (CRM). The book is a self-contained presentation, completely devoted to the Hodge conjecture and related topics. It includes many examples, and most results are completely proven or sketched. The motivation behind many of the results and background material is provided. This comprehensive approach to the book gives it a ``user-friendly'' style. Readers need not search elsewhere for various results. The book is suitable for use as a text for a topics course in algebraic geometry; includes an appendix by B. Brent Gordon.
Mixed Hodge Structures
Author | : Chris A.M. Peters,Joseph H. M. Steenbrink |
Publsiher | : Springer Science & Business Media |
Total Pages | : 467 |
Release | : 2008-02-27 |
Genre | : Mathematics |
ISBN | : 9783540770176 |
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This is comprehensive basic monograph on mixed Hodge structures. Building up from basic Hodge theory the book explains Delingne's mixed Hodge theory in a detailed fashion. Then both Hain's and Morgan's approaches to mixed Hodge theory related to homotopy theory are sketched. Next comes the relative theory, and then the all encompassing theory of mixed Hodge modules. The book is interlaced with chapters containing applications. Three large appendices complete the book.
Chow Rings Decomposition of the Diagonal and the Topology of Families AM 187
Author | : Claire Voisin |
Publsiher | : Princeton University Press |
Total Pages | : 171 |
Release | : 2014-02-23 |
Genre | : Mathematics |
ISBN | : 9780691160511 |
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In this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The volume is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by Voisin. The book focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by Voisin looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.
A Course in Hodge Theory
Author | : Hossein Movasati |
Publsiher | : Unknown |
Total Pages | : 0 |
Release | : 2021 |
Genre | : Hodge theory |
ISBN | : 157146400X |
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Offers an examination of the precursors of Hodge theory: first, the studies of elliptic and abelian integrals by Cauchy, Abel, Jacobi, and Riemann; and then the studies of two-dimensional multiple integrals by Poincare and Picard. The focus turns to the Hodge theory of affine hypersurfaces given by tame polynomials.
Conjectures in Arithmetic Algebraic Geometry
Author | : Wilfred W. J. Hulsbergen |
Publsiher | : Springer Science & Business Media |
Total Pages | : 246 |
Release | : 2013-06-29 |
Genre | : Technology & Engineering |
ISBN | : 9783663095057 |
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In the early 1980's, stimulated by work of Bloch and Deligne, Beilinson stated some intriguing conjectures on special values of L-functions of algebraic varieties defined over number fields. Roughly speaking these special values are determinants of higher regulator maps relating the higher algebraic K-groups of the variety to its cohomology. In this respect, higher algebraic K-theory is believed to provide a universal, motivic cohomology theory and the regulator maps are determined by Chern characters from higher algebraic K-theory to any other suitable cohomology theory. Also, Beilinson stated a generalized Hodge conjecture. This book provides an introduction to and a survey of Beilinson's conjectures and an introduction to Jannsen's work with respect to the Hodge and Tate conjectures. It addresses mathematicians with some knowledge of algebraic number theory, elliptic curves and algebraic K-theory.
Frobenius Distributions Lang Trotter and Sato Tate Conjectures
Author | : David Kohel,Igor Shparlinski |
Publsiher | : American Mathematical Soc. |
Total Pages | : 238 |
Release | : 2016-04-26 |
Genre | : Curves, Algebraic |
ISBN | : 9781470419479 |
Download Frobenius Distributions Lang Trotter and Sato Tate Conjectures Book in PDF, Epub and Kindle
This volume contains the proceedings of the Winter School and Workshop on Frobenius Distributions on Curves, held from February 17–21, 2014 and February 24–28, 2014, at the Centre International de Rencontres Mathématiques, Marseille, France. This volume gives a representative sample of current research and developments in the rapidly developing areas of Frobenius distributions. This is mostly driven by two famous conjectures: the Sato-Tate conjecture, which has been recently proved for elliptic curves by L. Clozel, M. Harris and R. Taylor, and the Lang-Trotter conjecture, which is still widely open. Investigations in this area are based on a fine mix of algebraic, analytic and computational techniques, and the papers contained in this volume give a balanced picture of these approaches.
Recent Advances in Hodge Theory
Author | : Matt Kerr,Gregory Pearlstein |
Publsiher | : Cambridge University Press |
Total Pages | : 533 |
Release | : 2016-02-04 |
Genre | : Mathematics |
ISBN | : 9781107546295 |
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Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.