Related papers: Chow-Lefschetz motives
We introduce a new algebraic-cycle model for the motivic cohomology theory of truncated polynomials $k[t]/(t^m)$ in one variable. This approach uses ideas from the deformation theory and non-archimedean analysis, and is distinct from the…
We describe Somekawa's K-group associated to a finite collection of semi-abelian varieties (or more general sheaves) in terms of the tensor product in Voevodsky's category of motives. While Somekawa's definition is based on Weil…
Interacting particles on graphs are routinely used to study magnetic behaviour in physics, disease spread in epidemiology, and opinion dynamics in social sciences. The literature on mean-field approximations of such systems for large graphs…
We introduce a cohomology theory for a class of projective varieties over a finite field coming from the canonical trace on a C*-algebra attached to the variety. Using the cohomology, we prove the rationality, functional equation and the…
In the mid sixties, A. Grothendieck envisioned a vast generalization of Galois theory to systems of polynomials in several variables, motivic Galois theory, and introduced tannakian categories on this occasion. In characteristic zero,…
In a previous work, the author have built two families of distinguished algebraic cycles in Bloch-Kriz cubical cycle complex over the projective line minus three points. The goal of this paper is to show how these cycles induce well-defined…
The Beilinson-Bloch type conjectures predict that the low degree rational Chow groups of intersections of quadrics are one dimensional. This conjecture was proved by Otwinowska. Making use of homological projective duality and the recent…
We construct an intermediate cohmology between motivic cohomology and Weil-etale cohomology. Using this, the Bass conjecture on finite generation of motivic cohomology, and the Beilinson-Tate on the finite generation of Weil-etale…
A remarkable result of Peter O'Sullivan asserts that the algebra epimorphism from the rational Chow ring of an abelian variety to its rational Chow ring modulo numerical equivalence admits a (canonical) section. Motivated by Beauville's…
We derive a version of the Rothenberg-Steenrod, fiber-to-base, spectral sequence for cohomology theories represented in model categories of simplicial presheaves. We then apply this spectral sequence to calculate the equivariant motivic…
We analyse scale anomalies in Lifshitz field theories, formulated as the relative cohomology of the scaling operator with respect to foliation preserving diffeomorphisms. We construct a detailed framework that enables us to calculate the…
Let G be a split semisimple linear algebraic group over a field k0. Let E be a G-torsor over a field extension k of k0. Let h be an algebraic oriented cohomology theory in the sense of Levine-Morel. Consider a twisted form E/B of the…
We define a generalisation of the completed Riemann zeta function in several complex variables. It satisfies a functional equation, shuffle product identities, and has simple poles along finitely many hyperplanes, with a recursive structure…
Substructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar,…
This thesis is concerned with the mixed Tate property of reductive algebraic groups $G$, which in particular guarantees a Chow Kunneth property for the classifying space $BG$. Toward this goal, we first refine the construction of the…
Given a hypersurface $X\subset \mathbb{P}^{N+1}_{\mathbb{C}}$ Dimca gave a proof showing that the cohomologies of X are the same as the projective space in a range determined by the dimension of the singular locus of X. We prove the analog…
This is my habilitation thesis. As the tradition wants, I tried to give an introduction of my field of research. I post it on the ArXiv with the hope it can be useful to young researchers looking for a short and friendly text on…
We investigate the relation of countable closed subsets of the reals with respect to continuous monotone embeddability; we show that there are exactly aleph_1 many equivalence classes with respect to this embeddability relation. This is an…
We prove that Lefschetz's principle of approximating the cohomology of a possibly singular affine scheme of finite type over a field by the cohomology of a suitable (thickening of a) hyperplane section can be made uniform: in the affine…
We investigate several interrelated foundational questions pertaining to the study of motivic dga's of Dan-Cohen--Schlank [8] and Iwanari [13]. In particular, we note that morphisms of motivic dga's can reasonably be thought of as a…