quasars

QSO Hosts and their Environments

by Isabel Márquez (Editor), et al

(Hardcover - December 1, 2001)

Observations of the starlike objects 3C 273, 3C 279, 3C 345

and of Sco X-1 with a scanning dual-beam polarimeter

(Bulletin / Lowell Observatory) by Aina Elvius (Author)

Contemporaneous IUE, EUVE, and high-energy observations of 3C 273

(SuDoc NAS 1.26:207861) by NASA

Chandra reveals a double-sided X-ray jet in the quasar 3C9 at z=2.012

Transfers, and Motivic Homology Theories by Vladimir Voevodsky, Andrei Suslin, and Eric M. Friedlander, Annals of Mathematics Studies, No. 143, Princeton University Press, NJ, 254 pages, ISBN 0-691-04815-0When thinking about this book, three questions come to mind: What are motives? What is motivic cohomology? How does this book fit into these frameworks? Let me begin with a very brief answer to these questions. The theory of motives is a branch of algebraic geometry dealing with algebraic varieties over a fixed field, k. The basic idea is simple: enlarge the category of varieties into one which is abelian, meaning that it resembles the category of abelian groups: we should be able to add morphisms, take kernels and cokernels of maps, etc. The objects in this enlarged category are to be called motives, whence the notion of the motive associated to an algebraic variety. Any reasonable cohomology theory on varieties should factor through this category of motives. Even better, the abelian nature of motives allows us to do homological algebra. In particular, we can use extension groups to form a universal cohomology theory for varieties. Not only does this motivate our interest in motives, but the universal property also gives rise to the play on words "motivic cohomology". Different ways of thinking about varieties leads to different classes of motives and different aspects of the theory. And each aspect of the theory quickly leads us into conjectural territory. The best understood part of the theory is the abelian category of pure motives. This is what we get by restricting our attention to smooth projective varieties, identifying numerically equivalent maps and taking coefficients in the rational numbers Q. The pure motives of smooth projective varieties are the analogues of semisimple modules over a finite-dimensional Q-algebra. The theory of pure motives is related to many deep unsolved problems in algebraic geometry, via what are known as the standard conjectures. At the other extreme, we have the most general part of the theory of motives, obtained by considering all varieties and taking coefficients in the integers Z... K-Theory Collection