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Moments, Monodromy, and Perversity: A Diophantine Perspective
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Nicholas M Katz
It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably "pure" algebro-geometric families of character sums over finite fields (and of their associated L-functions). Roughly speaking, Deligne showed that any such family ...
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Rigid Local Systems
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Nicholas M Katz
Riemann introduced the concept of a 'local system' on P1 (a finite set of points) nearly 140 years ago. His idea was to study the nth order linear differential equations by studying the rank in local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, ...
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Local Cohomology: An Algebraic Introduction with Geometric Applications
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M P Brodmann, R y Sharp
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 ...
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Compatibility, Stability, and Sheaves
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J L Bueso, Bueso Bueso, P Jara
This title integrates fundamental techniques from algebraic geometry, localization theory and ring theory, and demonstrates how each topic is enhanced by interaction with others, providing new results within a common framework. In this title, technical conclusions are presented and illustrated with concrete examples.
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Sheaf theory
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Glen E. Bredon
This book is primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems." The parts of sheaf theory covered here are those areas important to algebraic topology. There are several innovations in this book. The concept of the "tautness" of a subspace is introduced and exploited ...
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Intersection Cohomology
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Armand Borel
This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983. This volume supplies an introduction to the piecewise linear and sheaf-theoretic versions of that ...
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Weil Conjectures, Perverse Sheaves and L'Adic Fourier Transform
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Reinhardt Kiehl, Rainer Weissauer
In this book the authors describe the important generalization of the original Weil conjectures, as given by P.Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf ...
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Topology of Singular Spaces and Constructible Sheaves
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Jorg Schurmann
Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces. The ...
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Sheaf Theory
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B R Tennison, N J Hitchin (Editor)
Sheaf theory provides a means of discussing many different kinds of geometric objects in respect of the connection between their local and global properties. It finds its main applications in topology and modern algebraic geometry where it has been used as a tool for solving, with great success, several long-standing problems. This text is based ...
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Introduction to Categories, Homological Algebra and Sheaf Cohomology
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Jan R Strooker
Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields. This textbook provides an introduction to these methods, describing their elements and illustrating them by examples.
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Asymptotic Analysis for Integrable Connections with Irregular Singular Points
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Hideyuki Majima
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Structure Sheaves Over a Noncommutative Ring
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Jonathan S. Golan
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Algebraic Cycles, Sheaves, Shtukas, and Moduli: Impanga Lecture Notes
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Piotr Pragacz (Editor)
The articles in this volume are devoted to:moduli of coherent sheaves; principal bundles and sheaves and their moduli; new insights into Geometric Invariant Theory; stacks of shtukas and their compactifications; algebraic cycles vs. commutative algebra; Thom polynomials of singularities; zero schemes of sections of vector bundles. The main purpose ...
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Relative Invariants of Sheaves
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Alain Verschoren
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Several Complex Variables VII
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Hans Grauert
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Applications of Sheaves
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M P Fourman (Editor), C J Mulvey (Editor), D S Scott (Editor)
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Residues and Duality
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Robin Hartshorne
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Several Complex Variables VII: Sheaf-Theoretical Methods in Complex Analysis
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Hans Grauert, T Peternell (Contributions by), R Remmert (Contributions by)
This volume of the Encyclopaedia offers a systematic introduction and a comprehensive survey of the theory of complex spaces. It covers topics like semi-normal complex spaces, cohomology, the Levi problem, q-convexity and q-concavity. It is the first survey of this kind. The authors are internationally known outstanding experts who developed ...
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Equivariant Sheaves and Functors
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Joseph Bernstein
Introducing the equivariant derived category of sheaves, this monograph also provides applications to the equivariant intersection cohomology. This theory should benefit specialists in representation theory, algebraic geometry or topology.
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Factorizable Sheaves and Quantum Groups
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Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman
The book is devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity. These representations are realized as some spaces of vanishing cycles of perverse sheaves over configuration spaces. As an application, the bundles of conformal blocks over the moduli spaces of curves are studied. The ...
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Virtual Topology and Functor Geometry
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by
Fred Van Oystaeyen
In today's research, intrinsically noncommutative spaces are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it seems necessary to have a concept of space and its geometry that is fundamentally noncommutative. "Virtual Topology and ...
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Models for Smooth Infinitesimal Analysis
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Ieke Moerdijk, Gonzalo E Reyes
The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology ...
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Etale Cohomology
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J. S. Milne
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Twenty-Four Hours of Local Cohomology
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Srikanth Iyengar
This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Grobner ...
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Localization and sheaves : a relative point of view
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P. Jara, A. Verschoren, C. Vidal
This book completely solves the problem of representing rings (and modules over them), which are locally noetherian over subsets of their prime spectrum by structure sheaves over this subset. In order to realise this, one has to develop the necessary localization theory as well as to study local equivalents of familiar concepts like the Artin-Rees ...
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