Author | Huber, Annette. author |
---|---|

Title | Mixed Motives and Their Realization in Derived Categories [electronic resource] / by Annette Huber |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1995 |

Connect to | http://dx.doi.org/10.1007/BFb0095503 |

Descript | XVI, 216 p. online resource |

SUMMARY

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

CONTENT

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 Kรผnneth 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

Mathematics
Algebraic geometry
K-theory
Number theory
Mathematics
Algebraic Geometry
K-Theory
Number Theory