Related papers: f-categories and Tate motives

Consider the neutral Tannakian category mixed Tate motives over Z, in this paper we suggest a way to understand the structure of depth-graded motivic Lie subalgebra generated by the depth one part. We will show that from an isomorphism…

For each field k, we define an abelian category of rationally decomposed mixed motives with integer coefficients. When k is finite, we show that the category is Tannakian, and we prove formulas relating the behaviour of zeta functions near…

We give the first examples of finite groups G such that the Chow ring of the classifying space BG depends on the base field, even for fields containing the algebraic closure of Q. As a tool, we give several characterizations of the…

Let $f$ be a cuspidal eigenform of weight two and level $N$, let $p\nmid N$ be a prime at which $f$ is congruent to an Eisenstein series and let $V_f$ denote the $p$-adic Tate module of $f$. Beilinson constructed a class $\kappa_f\in…

We define the category of mixed Tate motives over the ring of S-integers of a number field. We define the motivic fundamental group (made unipotent) of a unirational variety over a number field. We apply this to the study of the motivic…

We show that the Tate conjecture for divisors over a finite field $\mathbb F$ is equivalent to an explicit algebraic problem about the third Milnor K-group of the function field $\bar {\mathbb F}(x,y,z)$ in three variables over $\bar…

Let $k$ be a perfect field of characteristic $p>0$. In this paper, without assuming resolution of singularities, we prove that the triangulated category of motives with modulus with rational coefficients is equivalent to Voevodsky's…

We formulate a conjectural p-adic analogue of Borel's theorem relating regulators for higher K-groups of number fields to special values of the corresponding zeta-functions, using syntomic regulators and p-adic L-functions. We also…

We show that the cellular objects in the module category over a motivic E infinity ring spectrum E can be described as the module category over a graded topological spectrum if E is strongly periodizable in our language. A similar statement…

We define Euclidean scissor congruence groups for an arbitrary algebraically closed field F and propose their conjectural description. We suggest how they should be related to mixed Tate motives over dual numbers for F.

We prove 2-out-of-3 property for rationality of motivic zeta function in distinguished triangles in Voevodsky's category DM. As an application, we show rationality of motivic zeta functions for all varieties whose motives are in the thick…

We define a theory of etale motives over a noetherian scheme. This provides a system of categories of complexes of motivic sheaves with integral coefficients which is closed under the six operations of Grothendieck. The rational part of…

We develop Milne's theory of Lefschetz motives for general adequate equivalence relations and over a not necessarily algebraically closed base field. The corresponding categories turn out to enjoy all properties predicted by standard and…

The Tate conjecture predicts that Galois-invariant classes in $\ell$-adic cohomology, and Frobenius-invariant classes in crystalline cohomology, arise from algebraic cycles. We prove an unconditional p-adic analogue of this principle in the…

We classify the localizing tensor ideals of the derived categories of mixed Tate motives over certain algebraically closed fields. More precisely, we prove that these categories are stratified in the sense of Barthel, Heard and Sanders. A…

This paper proves the Beilinson-Soul{\'e} vanishing conjecture for motives attached to the moduli spaces of curves of genus 0 with n marked points. As part of the proof, it is also proved that these motives are mixed Tate. As a consequence…

We introduce the notion of log motivic triangulated categories, which is the theoretical framework for understanding the motivic aspect of cohomology theories for fs log schemes. Then we study the Grothendieck six operations formalism for…

We refine the geometric Satake equivalence due to Ginzburg, Beilinson-Drinfeld, and Mirkovi\'c-Vilonen to an equivalence between mixed Tate motives on the double quotient $L^+ G \backslash LG / L^+ G$ and representations of Deligne's…

The first author has recently shown that semisimple algebraic groups are classified up to motivic equivalence by the local versions of the classical Tits indexes over field extensions, known as Tits p-indexes. We provide in this article the…

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…