Related papers: Notes on Artin-Tate motives

We give a brief introduction to tensor triangulated geometry, a brief introduction to various motivic categories, and then make some observations about the conjectural structure of the tensor triangulated spectrum of the Morel-Voevodsky…

We study the multiplicities of pure motives modulo numerical equivalence, which are defined as scalars comparing the tannakian trace with the ring-theoretic trace. Our general set-up is that of a rigid semi-simple tensor category such that…

We establish the group-theoretic classification of Sato-Tate groups of self-dual motives of weight 3 with rational coefficients and Hodge numbers h^{3,0} = h^{2,1} = h^{1,2} = h^{0,3} = 1. We then describe families of motives that realize…

We describe the heart of the canonical $t$-structure on the perfect derived category of a strictly positive graded algebra as the module category over the quadratic dual. Applying this result we obtain examples showing new phenomena on…

We study a family of mixed Tate motives over $\mathbb{Z}$ whose periods are linear forms in the zeta values $\zeta(n)$. They naturally include the Beukers-Rhin-Viola integrals for $\zeta(2)$ and the Ball-Rivoal linear forms in odd zeta…

We apply the structure theory of finite dimensional algebras in order to deduce dimension formulas for spaces of period numbers, i.e., complex numbers defined by integrals of algebraic nature. We get a complete and conceptually clear answer…

The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the value at one of these L-series encode arithmetic informations of certain Drinfeld modules…

We construct the Chow weight structure on the derived category of geometric motives with arbitrary coefficients for X a finite type scheme over a field characteristic 0 and G an affine algebraic group. In particular we also show that the…

The main goal of this paper is to study relative versions of the category of modules over the isotropic motivic Brown-Peterson spectrum, with a particular emphasis on their cellular subcategories. Using techniques developed by Levine, we…

The main goal of this paper is to define the so-called Chow weight structure for the category of Beilinson motives over any 'reasonable' base scheme $S$ (this is the version of Voevodsky's motives over $S$ defined by Cisinski and Deglise).…

In the arithmetic of function fields Drinfeld modules play the role that elliptic curves take on in the arithmetic of number fields. As higher dimensional generalizations of Drinfeld modules, and as the appropriate analogues of abelian…

We study the t-structure induced by an n-tilting module T in the derived category D(R) of a ring R. Our main objective is to determine when the heart of the t-structure is a Grothendieck category. We obtain characterizations in terms of…

The stable module category of a selfinjective algebra is triangulated, but need not have any nontrivial $t$-structures, and in particular, full abelian subcategories need not arise as hearts of a $t$-structure. The purpose of this paper is…

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 describe spaces of Bridgeland stability conditions on certain triangulated categories associated to Coxeter systems. These categories are defined algebraically using the category of modules for zigzag algebras associated to Coxeter…

We propose a refined version of the Beilinson-Bloch conjecture for the motive associated with a modular form of even weight. This conjecture relates the dimension of the image of the relevant p-adic Abel-Jacobi map to certain combinations…

We discuss the structure of integral etale motivic cohomology groups of smooth and projective schemes over algebraically closed fields, finite fields, local fields, and arithmetic schemes.

We define model category structures on the category of chain complexes over a Grothendieck abelian category depending on the choice of a generating family, and we study their behaviour with respect to tensor products and stabilization. This…

The manuscript at hand systematically studies K\"unneth formulas at a categorical level. We give criteria for an abstract six functor formalism to satisfy the categorical K\"unneth formula, and use this to formulate conjectures for…

In this article we initiate the study of the tensor triangular geometry of the categories Mot(k)_a and Mot(k)_l of non-commutative motives (over a base ring k). Since the full computation of the spectrum of Mot(k)_a and Mot(k)_l seems…