Homology of locally semialgebraic spaces / Hans Delfs
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1484Langue : anglais.Éditeur : Berlin : Springer-Verlag, 1991ISBN: 9783540546153.ISSN: 1617-9692.Sujet MSC : 14P10, Algebraic geometry - Real algebraic and real analytic geometry, Semialgebraic sets and related spaces14P25, Algebraic geometry - Real algebraic and real analytic geometry, Topology of real algebraic varieties
55N35, Homology and cohomology theories in algebraic topology, Other homology theories
55N30, Homology and cohomology theories in algebraic topology, Sheaf cohomologyEn-ligne : Springerlink | Zentralblatt | MathSciNet
... In chapter I a short introduction to the subject of abstract locally semialgebraic spaces is given.
Chapter II is devoted to the study of sheaves on abstract locally semialgebraic spaces. One of the main results is the following: The cohomology groups of these sheaves do not change when the base field is extended.
Chapter III deals with semi-algebraic Borel-Moore homology. Using combinatorial methods (with open simplices rather than closed ones) one can prove that every algebraic variety possesses a fundamental class. The use of sheaves allows to obtain results on Poincaré duality for arbitrary families of supports.
Chapter IV is devoted to some aspects of intersection theory for a general algebraically closed field of characteristic zero and some generalizations to this case of classical results are proved.
The book is very clear and well written. Many examples enlighten the results. (Zentralblatt)
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