02854nam 2200577 450 99646666960331620220908111753.03-540-49274-710.1007/BFb0095503(CKB)1000000000437203(SSID)ssj0000324859(PQKBManifestationID)12079268(PQKBTitleCode)TC0000324859(PQKBWorkID)10320822(PQKB)10251413(DE-He213)978-3-540-49274-0(MiAaPQ)EBC5592083(Au-PeEL)EBL5592083(OCoLC)1066181342(MiAaPQ)EBC6842356(Au-PeEL)EBL6842356(PPN)155174649(EXLCZ)99100000000043720320220908d1995 uy 0engurnn|008mamaatxtccrMixed motives and their realization in derived categories /Annette Huber1st ed. 1995.Berlin ;Heidelberg :Springer-Verlag,[1995]©19951 online resource (XVI, 216 p.) Lecture Notes in Mathematics ;Volume 1604Bibliographic Level Mode of Issuance: Monograph3-540-59475-2 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.Lecture notes in mathematics (Springer-Verlag) ;Volume 1604.Motives (Mathematics)Motives (Mathematics)516.35Huber Annette61000MiAaPQMiAaPQMiAaPQBOOK996466669603316Mixed motives and their realization in derived categories78095UNISA