Rational mixed Tate motivic graphs
نویسندگان
چکیده
منابع مشابه
Rational Tate classes
In despair, as Deligne (2000) put it, of proving the Hodge and Tate conjectures, we can try to find substitutes. For abelian varieties in characteristic zero, Deligne (1982) constructed a theory of Hodge classes having many of the properties that the algebraic classes would have if the Hodge conjecture were known. In this article I investigate whether there exists a theory of “rational Tate cla...
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Using the theory of mixed perverse sheaves, we extend arguments on the Hodge conjecture initiated by Lefschetz and Griffiths to the case of the Tate conjecture, and show that the Tate conjecture for divisors is closely related to the de Rham conjecture for nonproper varieties, finiteness of the Tate-Shafarevich groups, and also to some conjectures in the analytic number theory. Dedicated to Joh...
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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...
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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...
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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...
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ژورنال
عنوان ژورنال: Annals of K-Theory
سال: 2017
ISSN: 2379-1691,2379-1683
DOI: 10.2140/akt.2017.2.451