منابع مشابه
The slice filtration and mixed Tate motives
Using the ”slice filtration”, defined by effectivity conditions on Voevodsky’s triangulated motives, we define spectral sequences converging to their motivic cohomology and étale motivic cohomology. These spectral sequences are particularly interesting in the case of mixed Tate motives as their E2-terms then have a simple description. In particular this yields spectral sequences converging to t...
متن کاملMultiple polylogarithms and mixed Tate motives
from analytic, Hodge-theoretic and motivic points of view. Let μN be the group of all N -th roots of unity. One of the reasons to develop such a theory was a mysterious correspondence (loc. cit.) between the structure of the motivic fundamental group π 1 (Gm − μN ) and the geometry and topology of modular varieties Y1(m;N) := Γ1(m;N)\GLm(R)/R ∗ + ·Om Here Γ1(m;N) ⊂ GLm(Z) is the subgroup fixing...
متن کاملMixed Artin–Tate motives over number rings
This paper studies Artin–Tate motives over bases S ⊂ Spec OF , for a number field F . As a subcategory of motives over S, the triangulated category of Artin–TatemotivesDATM(S) is generated by motives φ∗1(n), where φ is any finite map. After establishing the stability of these subcategories under pullback and pushforward along open and closed immersions, a motivic t-structure is constructed. Exa...
متن کاملVolumes of hyperbolic manifolds and mixed Tate motives
1. Volumes of (2n − 1)-dimensional hyperbolic manifolds and the Borel regulator on K2n−1(Q). Let M be an n-dimensional hyperbolic manifold with finite volume vol(M). If n = 2m is an even number, then by the Gauss-Bonnet theorem ([Ch]) vol(M) = −c2m · χ(M) where c2m = 1/2×(volume of sphere S of radius 1) and χ(M) is the Euler characteristic of M. This is straightforward for compact manifolds and...
متن کاملLefschetz Motives and the Tate Conjecture
A Lefschetz class on a smooth projective variety is an element of the Q-algebra generated by divisor classes. We show that it is possible to define Q-linear Tannakian categories of abelian motives using the Lefschetz classes as correspondences, and we compute the fundamental groups of the categories. As an application, we prove that the Hodge conjecture for complex abelian varieties of CM-type ...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2015
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnv239