Coherent Sheaves On Varieties Arising In Springer Theory And Category 0
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Coherent Sheaves On Varieties Arising In Springer Theory And Category 0
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Author : Vinoth Nandakumar
language : en
Publisher:
Release Date : 2015
Coherent Sheaves On Varieties Arising In Springer Theory And Category 0 written by Vinoth Nandakumar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
In this thesis, we will study three topics related to Springer theory (specifically, the geometry of the exotic nilpotent cone, and two-block Springer fibers), and stability conditions for category 0. In the first chapter, we will be studying the geometry of the exotic nilpotent cone (which is a variant of the nilpotent cone in type C introduced by Kato). Bezrukavnikov has established a bijection between A+, the dominant weights for an arbitrary simple algebraic group H, and 0, the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit (as originally conjectured by Lusztig and Vogan). Here we prove an analogous statement for the exotic nilpotent cone. In the second chapter (which is based on joint work with Rina Anno), we study the exotic t-structure for a two-block Springer fibre (i.e. for a nilpotent matrix of type (m + n, n) in type A). The exotic t-structure has been defined by Bezrukavnikov and Mirkovic for Springer theoretic varieties in order to study representations of Lie algebras in positive characteristic. Using techniques developed by Cautis and Kamnitzer, we show that the irreducible objects in the heart of the exotic t-structure are indexed by crossingless (m, m + 2n) matchings. We also show that the resulting Ext algebras resemble Khovanov's arc algebras (but placed on an annulus). In the third chapter, we study stability conditions on certain sub-quotients of category 0. Recently, Anno, Bezrukavnikov and Mirkovic have introduced the notion of a "real variation of stability conditions" (which are related to Bridgeland's stability conditions), and construct an example using categories of coherent sheaves on Springer fibers. Here we construct another example, by studying certain sub-quotients of category 0 with a fixed Gelfand-Kirillov dimension. We use the braid group action on the derived category of category 0, and certain leading coefficient polynomials coming from translation functors.
Recent Developments In Algebraic And Combinatorial Aspects Of Representation Theory
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Author : Vyjayanthi Chari
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-11-25
Recent Developments In Algebraic And Combinatorial Aspects Of Representation Theory written by Vyjayanthi Chari and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-25 with Mathematics categories.
This volume contains the proceedings of the International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, held August 12-16, 2010, at the National Institute of Advanced Studies, Bangalore, India, and the follow-up conference held May 18-20, 2012, at the University of California, USA. It contains original research and survey articles on various topics in the theory of representations of Lie algebras, quantum groups and algebraic groups, including crystal bases, categorification, toroidal algebras and their generalisations, vertex algebras, Hecke algebras, Kazhdan-Lusztig bases, $q$-Schur algebras, and Weyl algebras.
Algebra Arithmetic And Geometry
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Author : Yuri Tschinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-05
Algebra Arithmetic And Geometry written by Yuri Tschinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-05 with Mathematics categories.
EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-12-20
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Mathematics categories.
Recent Developments In Lie Algebras Groups And Representation Theory
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Author : Kailash C. Misra
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Recent Developments In Lie Algebras Groups And Representation Theory written by Kailash C. Misra and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book contains the proceedings of the 2009-2011 Southeastern Lie Theory Workshop Series, held October 9-11, 2009 at North Carolina State University, May 22-24, 2010, at the University of Georgia, and June 1-4, 2011 at the University of Virginia. Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.
Cohomological And Geometric Approaches To Rationality Problems
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Author : Fedor Bogomolov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-03
Cohomological And Geometric Approaches To Rationality Problems written by Fedor Bogomolov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-03 with Mathematics categories.
Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov
Around Langlands Correspondences
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Author : Farrell Brumley
language : en
Publisher: American Mathematical Soc.
Release Date : 2017
Around Langlands Correspondences written by Farrell Brumley and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Algebraic number theory categories.
This volume contains the proceedings of the international conference ``Around Langlands Correspondences'', held from June 17-20, 2015, at Universite Paris Sud in Orsay, France. The Langlands correspondence (nowadays called the usual Langlands correspondence), conjectured by Robert Langlands in the late 1960s and early 1970s, has recently seen some new mysterious generalizations: the modular Langlands correspondence, the $p$-adic Langlands correspondence, and the geometric Langlands correspondence, the last of which seems to share deep connections with the Baum-Connes conjecture. The aim of this volume is to present, through a mix of research and expository articles, some of the fascinating new directions in number theory and representation theory arising from recent developments in the Langlands program. Special emphasis is placed on nonclassical versions of the conjectural Langlands correspondences, where the underlying field is no longer the complex numbers.
Algebraic Geometry Ii Cohomology Of Schemes
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Author : Ulrich Görtz
language : en
Publisher: Springer Nature
Release Date : 2023-11-22
Algebraic Geometry Ii Cohomology Of Schemes written by Ulrich Görtz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-22 with Mathematics categories.
This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.
Encyclopaedia Of Mathematics
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Author : M. Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by M. Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.