Filtrations On The Homology Of Algebraic Varieties

Author : Eric M. Friedlander,Barry Mazur
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 55,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825914

Get Book

Filtrations on the Homology of Algebraic Varieties by Eric M. Friedlander,Barry Mazur Pdf

This work provides a detailed exposition of a classical topic from a very recent viewpoint. Friedlander and Mazur describe some foundational aspects of ``Lawson homology'' for complex projective algebraic varieties, a homology theory defined in terms of homotopy groups of spaces of algebraic cycles. Attention is paid to methods of group completing abelian topological monoids. The authors study properties of Chow varieties, especially in connection with algebraic correspondences relating algebraic varieties. Operations on Lawson homology are introduced and analyzed. These operations lead to a filtration on the singular homology of algebraic varieties, which is identified in terms of correspondences and related to classical filtrations of Hodge and Grothendieck.

Author : Andrew H. Wallace
Publisher : Courier Corporation
Page : 129 pages
File Size : 43,9 Mb
Release : 2015-01-14
Category : Mathematics
ISBN : 9780486787848

Get Book

Homology Theory on Algebraic Varieties by Andrew H. Wallace Pdf

Concise and authoritative monograph, geared toward advanced undergraduate and graduate students, covers linear sections, singular and hyperplane sections, Lefschetz's first and second theorems, the Poincaré formula, and invariant and relative cycles. 1958 edition.

Author : B. Brent Gordon
Publisher : American Mathematical Soc.
Page : 468 pages
File Size : 44,6 Mb
Release : 2000-01-01
Category : Mathematics
ISBN : 0821870203

Get Book

The Arithmetic and Geometry of Algebraic Cycles by B. Brent Gordon Pdf

From the June 1998 Summer School come 20 contributions that explore algebraic cycles (a subfield of algebraic geometry) from a variety of perspectives. The papers have been organized into sections on cohomological methods, Chow groups and motives, and arithmetic methods. Some specific topics include logarithmic Hodge structures and classifying spaces; Bloch's conjecture and the K-theory of projective surfaces; and torsion zero-cycles and the Abel-Jacobi map over the real numbers.

Author : Andrew Hugh Wallace
Publisher : Unknown
Page : 115 pages
File Size : 41,7 Mb
Release : 2024-06-28
Category : Homology theory
ISBN : LCCN:lc57014497

Get Book

Homology theory on algebraic varieties by Andrew Hugh Wallace Pdf

Author : János Kollár,David R. Morrison
Publisher : American Mathematical Soc.
Page : 469 pages
File Size : 51,8 Mb
Release : 1997
Category : Geometry, Algebraic
ISBN : 9780821808948

Get Book

Algebraic Geometry Santa Cruz 1995 by János Kollár,David R. Morrison Pdf

Author : I.R. Shafarevich
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 46,5 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9783642609251

Get Book

Algebraic Geometry II by I.R. Shafarevich Pdf

This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.

Author : Carlos Andradas,Jesús M. Ruiz
Publisher : American Mathematical Soc.
Page : 117 pages
File Size : 43,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821826126

Get Book

Algebraic and Analytic Geometry of Fans by Carlos Andradas,Jesús M. Ruiz Pdf

A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a description is possible locally around every point, by means of analytic inequalities varying with the point, the set is called semianalytic. If one single system of strict inequalities is enough, either globally or locally at every point, the set is called basic. The topic of this work is the relationship between these two notions. Namely, Andradas and Ruiz describe and characterize, both algebraically and geometrically, the obstructions for a basic semianalytic set to be basic semialgebraic. Then they describe a special family of obstructions that suffices to recognize whether or not a basic semianalytic set is basic semialgebraic. Finally, they use the preceding results to discuss the effect on basicness of birational transformations.

Author : Gavril Farkas,Gerard van der Geer,Mingmin Shen,Lenny Taelman
Publisher : Springer Nature
Page : 433 pages
File Size : 45,6 Mb
Release : 2021-10-19
Category : Mathematics
ISBN : 9783030754211

Get Book

Rationality of Varieties by Gavril Farkas,Gerard van der Geer,Mingmin Shen,Lenny Taelman Pdf

This book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces and birational invariants of group actions on varieties, contributed by the foremost experts in their fields. The question of whether an algebraic variety can be parametrized by rational functions of as many variables as its dimension has a long history and played an important role in the history of algebraic geometry. Recent developments in algebraic geometry have made this question again a focal point of research and formed the impetus to organize a conference in the series of conferences on the island of Schiermonnikoog. The book follows in the tradition of earlier volumes, which originated from conferences on the islands Texel and Schiermonnikoog.

Author : Eric Friedlander,Daniel R. Grayson
Publisher : Springer Science & Business Media
Page : 1148 pages
File Size : 42,8 Mb
Release : 2005-07-18
Category : Mathematics
ISBN : 9783540230199

Get Book

Handbook of K-Theory by Eric Friedlander,Daniel R. Grayson Pdf

This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.

Author : S.I. Gelfand,Yu.I. Manin
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 42,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642579110

Get Book

Homological Algebra by S.I. Gelfand,Yu.I. Manin Pdf

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.

Author : Greg Friedman
Publisher : Cambridge University Press
Page : 491 pages
File Size : 48,5 Mb
Release : 2011-03-28
Category : Mathematics
ISBN : 9780521191678

Get Book

Topology of Stratified Spaces by Greg Friedman Pdf

This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.

Author : S. Müller-Stach,C. Peters
Publisher : Cambridge University Press
Page : 314 pages
File Size : 41,9 Mb
Release : 2004-04-20
Category : Mathematics
ISBN : 0521545471

Get Book

Transcendental Aspects of Algebraic Cycles by S. Müller-Stach,C. Peters Pdf

Lecture notes for graduates or researchers wishing to enter this modern field of research.

Author : Bjørn Ian Dundas,Thomas G. Goodwillie,Randy McCarthy
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 54,8 Mb
Release : 2012-09-06
Category : Mathematics
ISBN : 9781447143932

Get Book

The Local Structure of Algebraic K-Theory by Bjørn Ian Dundas,Thomas G. Goodwillie,Randy McCarthy Pdf

Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.

Author : Shiing-Shen Chern
Publisher : World Scientific
Page : 278 pages
File Size : 55,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9812777415

Get Book

Contemporary Trends in Algebraic Geometry and Algebraic Topology by Shiing-Shen Chern Pdf

The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Prof S S Chern in Nankai Institute of Mathematics. It was devoted to memorializing those two outstanding and original Chinese mathematicians who had made significant contributions to algebraic geometry and algebraic topology, respectively. It also provided a forum for leading mathematicians to expound and discuss their views on new ideas in these fields, as well as trends in 21st Century mathematics. About 100 mathematicians participated in the conference, including Sir Michael Atiyah, Jacob Palis, Phillip Griffiths, David Eisenbud, Philippe Tondeur, Yujiro Kawamata, Tian Gang, etc.This invaluable volume contains the selected papers presented at the conference. The topics include canonical maps of Gorenstein 3-folds, fundamental groups of algebraic curves, Chen''s interated integrals, algebraic fiber spaces, and others.

Author : Andrew J. Blumberg,Teena Gerhardt,Michael A. Hill
Publisher : Cambridge University Press
Page : 441 pages
File Size : 44,7 Mb
Release : 2022-07-21
Category : Mathematics
ISBN : 9781009123297

Get Book

Stable Categories and Structured Ring Spectra by Andrew J. Blumberg,Teena Gerhardt,Michael A. Hill Pdf

A graduate-level introduction to the homotopical technology in use at the forefront of modern algebraic topology.