Local cohomology

About: Local cohomology is a research topic. Over the lifetime, 1326 publications have been published within this topic receiving 25931 citations.

Introduction to Homological Algebra

Abstract: The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician This book provides a unified account of homological algebra as it exists today The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described This book is suitable for second or third year graduate students The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences Homology of group and Lie algebras illustrate these topics Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra

Combinatorial Commutative Algebra

Abstract: Monomial Ideals.- Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional staircases.- Cellular resolutions.- Alexander duality.- Generic monomial ideals.- Toric Algebra.- Semigroup rings.- Multigraded polynomial rings.- Syzygies of lattice ideals.- Toric varieties.- Irreducible and injective resolutions.- Ehrhart polynomials.- Local cohomology.- Determinants.- Plucker coordinates.- Matrix Schubert varieties.- Antidiagonal initial ideals.- Minors in matrix products.- Hilbert schemes of points.

Local Cohomology: An Algebraic Introduction with Geometric Applications

Abstract: This book provides a careful and detailed algebraic introduction to Grothendieck’s local cohomology theory, and provides many illustrations of applications of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo–Mumford regularity, the Fulton–Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. It is designed for graduate students who have some experience of basic commutative algebra and homological algebra, and also for experts in commutative algebra and algebraic geometry.

Kac-Moody Groups, their Flag Varieties and Representation Theory

Abstract: Introduction * Kac--Moody Algebras -- Basic Theory * Representation Theory of Kac--Moody Algebras * Lie Algebra Homology and Cohomology * An Introduction to ind-Varieties and pro-Groups * Tits Systems -- Basic Theory * Kac--Moody Groups -- Basic Theory * Generalized Flag Varieties of Kac--Moody Groups * Demazure and Weyl--Kac Character Formulas * BGG and Kempf Resolutions * Defining Equations of G/P and Conjugacy Theorems * Topology of Kac-Moody Groups and Their Flag Varieties * Smoothness and Rational Smoothness of Schubert Varieties * An Introduction to Affine Kac-Moody Lie Algebras and Groups * Appendix A. Results from Algebraic Geometry * Appendix B. Local Cohomology * Appendix C. Results from Topology * Appendix D. Relative Homological Algebra * Appendix E. An Introduction to Spectral Sequences * Bibliography * Index of Notation * Index