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.
http://dx.doi.org/10.1090/surv/057/02 CHAPTER II Motivic Cohomology and Higher Chow Groups In [19], Bloch defines his higher Chow groups as a candidate for a reasonable theory of motivic cohomology. In this chapter, we extend and modify ...
This handbook offers a compilation of techniques and results in K-theory. These two volumes consist of chapters, each of which is dedicated to a specific topic and is written by a leading expert.
An even better language to describe periods is the language of motives. The concept was introduced by Grothendieck in his approach to the Weil conjectures. Philosophically, motives are objects in a universal abelian category attached to ...
... categories of motives as indeed it “kills” Tate twists (this is compatible with Remark 6.2). Remark 6.4 K, then RB ... realization → RigDA functor ́et (K) from that RigDA characteristic. ́et (K) with Any values such realization in Q ...
For young people beginning research, this is even more important, so these are a must for any serious mathematics library.
... motives defined by Voevodsky and Nori. PhD thesis, Albert-Ludwigs-Universit ̈at Freiburg, 2016. arXiv:1609.05516 ... Mixed motives and their realization in derived categories, Lecture Notes in Mathematics 1604. Springer-Verlag, Berlin ...
... Mixed Motives and Their Realization in Derived Categories " , LNM 1604 , Springer 1995 . A. Huber , " Mixed perverse sheaves for schemes over number fields " , Comp . Math . 108 ( 1997 ) , 107–121 . A. Huber , J. Wildeshaus ...
... Mixed Hodge polynomials of character varieties. Invent. Math. 174(3), 555–624. With an appendix by Nicholas M. Katz ... motives. Ann. Inst. Fourier (Grenoble) 57(6), 1927–1945 H. Hironaka (1964), Resolution of singularities of an ...
Historically, this book is the first to give a complete construction of a triangulated category of mixed motives with rational coefficients satisfying the full Grothendieck six functors formalism as well as fulfilling Beilinson’s program, ...
... Classification of Threedimensional Homogeneous Complex Manifolds. XI, 230 pages. 1995. Vol. 1603: V. Ene, Real Functions — Current Topics. XIII, 310 pages. 1995. Vol. 1604: A. Huber, Mixed Motives and their Realization in Derived Categories ...