Download or read book Filtrations on the Homology of Algebraic Varieties written by Eric M. Friedlander and published by American Mathematical Soc.. This book was released on 1994 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 analysed. 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.
Download or read book Filtrations on the Homology of Algebraic Varieties written by Eric M. Friedlander and published by . This book was released on 1994 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Arithmetic and Geometry of Algebraic Cycles written by B. Brent Gordon and published by American Mathematical Soc.. This book was released on 2000-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Homology Cohomology And Sheaf Cohomology For Algebraic Topology Algebraic Geometry And Differential Geometry written by Jean H Gallier and published by World Scientific. This book was released on 2022-01-19 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.
Download or read book On the De Rham Cohomology of Algebraic Varieties written by Robin Hartshorne and published by . This book was released on 1975 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rational Points on Varieties written by Bjorn Poonen and published by American Mathematical Soc.. This book was released on 2017-12-13 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.
Download or read book Algebraic Geometry II written by I.R. Shafarevich and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-11-11 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Singularities I written by Jean-Paul Brasselet and published by American Mathematical Soc.. This book was released on 2008 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Geometry written by H. Kurke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Conference on Algebraic Geometry, held in Berlin 9-15 March 1988, was organised by the Sektion Mathematik of the Humboldt-Universitat. The organising committee consisted of H. Kurke, W. Kleinert, G. Pfister and M. Roczen. The Conference is one in a series organised by the Humboldt-Universitat at regular intervals of two or three years, with the purpose of providing a meeting place for mathematicians from eastern and western countries. The present volume contains elaborations of part of the lectures presented at the Conference and some articles on related subjects. All papers were subject to the regular refereeing procedure of Compositio Mathematica, and H. Kurke acted as a guest editor of this journal. The papers focus on actual themes in algebraic geometry and singularity theory, such as vector bundles, arithmetical algebraic geometry, intersection theory, moduli and Hodge theory. We are grateful to all those who, by their hospitality, their presence at the Con ference, their support or their written contributions, have made this Conference to a success. The editors Compositio Mathematica 76: viii, 1990.
Download or read book Homotopy Theory Relations with Algebraic Geometry Group Cohomology and Algebraic K Theory written by Paul Gregory Goerss and published by American Mathematical Soc.. This book was released on 2004 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.
Download or read book Topology of Stratified Spaces written by Greg Friedman and published by Cambridge University Press. This book was released on 2011-03-28 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.
Download or read book Algebraic Geometry Santa Cruz 1995 written by János Kollár and published by American Mathematical Soc.. This book was released on 1997 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hodge Theory MN 49 written by Eduardo Cattani and published by Princeton University Press. This book was released on 2014-07-21 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kähler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck’s algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne’s theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
Download or read book Rationality of Varieties written by Gavril Farkas and published by Springer Nature. This book was released on 2021-10-19 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bulletin of the American Mathematical Society written by and published by . This book was released on 1997 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt:
