Mixed Motives and Their Realization in Derived Categories
Huber, Annette.
Mixed Motives and Their Realization in Derived Categories [electronic resource] / by Annette Huber. - XVI, 216 p. online resource. - Lecture Notes in Mathematics, 1604 0075-8434 ; . - Lecture Notes in Mathematics, 1604 .
Basic notions -- Derived categories of exact categories -- Filtered derived categories -- Gluing of categories -- Godement resolutions -- Singular cohomology -- De Rham cohomology -- Hodge realization -- 1-adic cohomology -- Comparison functors: 1-adic versus singular realization -- The mixed realization -- The tate twist -- ?-product and internal hom on D MR -- The Künneth morphism -- The Bloch-Ogus axioms -- The Chern class of a line bundle -- Classifying spaces -- Higher Chern classes -- Operations of correspondences -- Grothendieck motives -- Polarizability -- Mixed motives.
The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. The monograph describes the approach to motives via their well-defined realizations. This includes a review of several known cohomology theories. A new absolute cohomology is introduced and studied. The book assumes knowledge of the standard cohomological techniques in algebraic geometry as well as K-theory. So the monograph is primarily intended for researchers. Advanced graduate students can use it as a guide to the literature.
9783540492740
10.1007/BFb0095503 doi
Geometry, algebraic.
K-theory.
Number theory.
Algebraic Geometry.
K-Theory.
Number Theory.
QA564-609
516.35
Mixed Motives and Their Realization in Derived Categories [electronic resource] / by Annette Huber. - XVI, 216 p. online resource. - Lecture Notes in Mathematics, 1604 0075-8434 ; . - Lecture Notes in Mathematics, 1604 .
Basic notions -- Derived categories of exact categories -- Filtered derived categories -- Gluing of categories -- Godement resolutions -- Singular cohomology -- De Rham cohomology -- Hodge realization -- 1-adic cohomology -- Comparison functors: 1-adic versus singular realization -- The mixed realization -- The tate twist -- ?-product and internal hom on D MR -- The Künneth morphism -- The Bloch-Ogus axioms -- The Chern class of a line bundle -- Classifying spaces -- Higher Chern classes -- Operations of correspondences -- Grothendieck motives -- Polarizability -- Mixed motives.
The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. The monograph describes the approach to motives via their well-defined realizations. This includes a review of several known cohomology theories. A new absolute cohomology is introduced and studied. The book assumes knowledge of the standard cohomological techniques in algebraic geometry as well as K-theory. So the monograph is primarily intended for researchers. Advanced graduate students can use it as a guide to the literature.
9783540492740
10.1007/BFb0095503 doi
Geometry, algebraic.
K-theory.
Number theory.
Algebraic Geometry.
K-Theory.
Number Theory.
QA564-609
516.35