Homology of Locally Semialgebraic Spaces [electronic resource] /
Locally semialgebraic spaces serve as an appropriate framework for studying the topological properties of varieties and semialgebraic sets over a real closed field. This book contributes to the fundamental theory of semialgebraic topology and falls into two main parts. The first dealswith sheaves and their cohomology on spaces which locally look like a constructible subset of a real spectrum. Topics like families of support, homotopy, acyclic sheaves, base-change theorems and cohomological dimension are considered. In the second part a homology theory for locally complete locally semialgebraic spaces over a real closed field is developed, the semialgebraic analogue of classical Bore-Moore-homology. Topics include fundamental classes of manifolds and varieties, Poincare duality, extensions of the base field and a comparison with the classical theory. Applying semialgebraic Borel-Moore-homology, a semialgebraic ("topological") approach to intersection theory on varieties over an algebraically closed field of characteristic zero is given. The book is addressed to researchers and advanced students in real algebraic geometry and related areas.
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Format: | Texto biblioteca |
Language: | eng |
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Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,
1991
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Subjects: | Mathematics., Algebraic geometry., Category theory (Mathematics)., Homological algebra., Topology., Algebraic topology., Category Theory, Homological Algebra., Algebraic Topology., Algebraic Geometry., |
Online Access: | http://dx.doi.org/10.1007/BFb0093939 |
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KOHA-OAI-TEST:2086762018-07-30T23:39:52ZHomology of Locally Semialgebraic Spaces [electronic resource] / Delfs, Hans. author. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,1991.engLocally semialgebraic spaces serve as an appropriate framework for studying the topological properties of varieties and semialgebraic sets over a real closed field. This book contributes to the fundamental theory of semialgebraic topology and falls into two main parts. The first dealswith sheaves and their cohomology on spaces which locally look like a constructible subset of a real spectrum. Topics like families of support, homotopy, acyclic sheaves, base-change theorems and cohomological dimension are considered. In the second part a homology theory for locally complete locally semialgebraic spaces over a real closed field is developed, the semialgebraic analogue of classical Bore-Moore-homology. Topics include fundamental classes of manifolds and varieties, Poincare duality, extensions of the base field and a comparison with the classical theory. Applying semialgebraic Borel-Moore-homology, a semialgebraic ("topological") approach to intersection theory on varieties over an algebraically closed field of characteristic zero is given. The book is addressed to researchers and advanced students in real algebraic geometry and related areas.Abstract locally semialgebraic spaces -- Sheaf theory on locally semialgebraic spaces -- Semialgebraic Borel-Moore-homology -- Some intersection theory.Locally semialgebraic spaces serve as an appropriate framework for studying the topological properties of varieties and semialgebraic sets over a real closed field. This book contributes to the fundamental theory of semialgebraic topology and falls into two main parts. The first dealswith sheaves and their cohomology on spaces which locally look like a constructible subset of a real spectrum. Topics like families of support, homotopy, acyclic sheaves, base-change theorems and cohomological dimension are considered. In the second part a homology theory for locally complete locally semialgebraic spaces over a real closed field is developed, the semialgebraic analogue of classical Bore-Moore-homology. Topics include fundamental classes of manifolds and varieties, Poincare duality, extensions of the base field and a comparison with the classical theory. Applying semialgebraic Borel-Moore-homology, a semialgebraic ("topological") approach to intersection theory on varieties over an algebraically closed field of characteristic zero is given. The book is addressed to researchers and advanced students in real algebraic geometry and related areas.Mathematics.Algebraic geometry.Category theory (Mathematics).Homological algebra.Topology.Algebraic topology.Mathematics.Category Theory, Homological Algebra.Algebraic Topology.Algebraic Geometry.Topology.Springer eBookshttp://dx.doi.org/10.1007/BFb0093939URN:ISBN:9783540384946 |
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Mathematics. Algebraic geometry. Category theory (Mathematics). Homological algebra. Topology. Algebraic topology. Mathematics. Category Theory, Homological Algebra. Algebraic Topology. Algebraic Geometry. Topology. Mathematics. Algebraic geometry. Category theory (Mathematics). Homological algebra. Topology. Algebraic topology. Mathematics. Category Theory, Homological Algebra. Algebraic Topology. Algebraic Geometry. Topology. |
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Mathematics. Algebraic geometry. Category theory (Mathematics). Homological algebra. Topology. Algebraic topology. Mathematics. Category Theory, Homological Algebra. Algebraic Topology. Algebraic Geometry. Topology. Mathematics. Algebraic geometry. Category theory (Mathematics). Homological algebra. Topology. Algebraic topology. Mathematics. Category Theory, Homological Algebra. Algebraic Topology. Algebraic Geometry. Topology. Delfs, Hans. author. SpringerLink (Online service) Homology of Locally Semialgebraic Spaces [electronic resource] / |
description |
Locally semialgebraic spaces serve as an appropriate framework for studying the topological properties of varieties and semialgebraic sets over a real closed field. This book contributes to the fundamental theory of semialgebraic topology and falls into two main parts. The first dealswith sheaves and their cohomology on spaces which locally look like a constructible subset of a real spectrum. Topics like families of support, homotopy, acyclic sheaves, base-change theorems and cohomological dimension are considered. In the second part a homology theory for locally complete locally semialgebraic spaces over a real closed field is developed, the semialgebraic analogue of classical Bore-Moore-homology. Topics include fundamental classes of manifolds and varieties, Poincare duality, extensions of the base field and a comparison with the classical theory. Applying semialgebraic Borel-Moore-homology, a semialgebraic ("topological") approach to intersection theory on varieties over an algebraically closed field of characteristic zero is given. The book is addressed to researchers and advanced students in real algebraic geometry and related areas. |
format |
Texto |
topic_facet |
Mathematics. Algebraic geometry. Category theory (Mathematics). Homological algebra. Topology. Algebraic topology. Mathematics. Category Theory, Homological Algebra. Algebraic Topology. Algebraic Geometry. Topology. |
author |
Delfs, Hans. author. SpringerLink (Online service) |
author_facet |
Delfs, Hans. author. SpringerLink (Online service) |
author_sort |
Delfs, Hans. author. |
title |
Homology of Locally Semialgebraic Spaces [electronic resource] / |
title_short |
Homology of Locally Semialgebraic Spaces [electronic resource] / |
title_full |
Homology of Locally Semialgebraic Spaces [electronic resource] / |
title_fullStr |
Homology of Locally Semialgebraic Spaces [electronic resource] / |
title_full_unstemmed |
Homology of Locally Semialgebraic Spaces [electronic resource] / |
title_sort |
homology of locally semialgebraic spaces [electronic resource] / |
publisher |
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, |
publishDate |
1991 |
url |
http://dx.doi.org/10.1007/BFb0093939 |
work_keys_str_mv |
AT delfshansauthor homologyoflocallysemialgebraicspaceselectronicresource AT springerlinkonlineservice homologyoflocallysemialgebraicspaceselectronicresource |
_version_ |
1756268555023679488 |