Related papers: On Chow weight structures without projectivity and…

In this PhD thesis we investigate the significance of Chow groups for zero mode counting and anomaly cancellation in F-theory vacua. The major part of this thesis focuses on zero mode counting. We explain that elements of Chow group…

For every smooth and separated Deligne-Mumford stack $F$, we associate a motive $M(F)$ in Voevodsky's category of mixed motives with rational coefficients $\mathbf{DM}^{\eff}(k,\mathbb{Q})$. When $F$ is proper over a field of characteristic…

In the present article we define an integral analogue of Chow-K\"unneth decomposition for \'etale motives. By using families of conservative functors we are able to establish a decomposition of the \'etale motive of commutative group…

We describe the Chow ring with rational coefficients of the moduli space of stable maps with marked points Mbar_{0,m}(n,d) as the subring of invariants of a ring B, relative to the action of the group of symmetries of d elements. B is…

Motivic cohomology is powerful tool in algebraic geometry with associated realization maps giving important information about the relations between cohomological invariants of schemes and their classifying spaces. The problem of computing…

By defining and studying functorial properties of the Borel-Moore motivic homology, we identify the heart of Bondarko-H\'ebert's weight structure on Beilinson motives with Corti-Hanamura's category of Chow motives over a base, therefore…

This paper is dedicated to new methods of constructing weight structures and weight-exact localizations; our arguments generalize their bounded versions considered in previous papers of the authors. We start from a class of objects $P$ of…

Let V be a cofibrantly generated closed symmetric monoidal model category and M a model V-category. We say that a weighted colimit W*D of a diagram D weighted by W is a homotopy weighted colimit if the diagram D is pointwise cofibrant and…

We study regularity in the context of ring spectra and spectral stacks. Parallel to that, we construct a weight structure on the category of compact quasi-coherent sheaves on spectral quotient stacks of the form $X=[\operatorname{Spec}…

We relate the notion of finite dimensionality of the Chow motive M(X) of a smooth projective variety X (as defined by S. Kimura) with the Conjectures of Beilinson, Bloch and Murre on the existence of a filtration on the Chow ring CH(X). We…

This book discusses the construction of triangulated categories of mixed motives over a noetherian scheme of finite dimension, extending Voevodsky's definition of motives over a field. In particular, it is shown that motives with rational…

In this article, we improve our main results from \emph{Chow groups and $L$-derivatives of automorphic motives for unitary groups} in two direction: First, we allow ramified places in the CM extension $E/F$ at which we consider…

In this paper we study properties of the Chow ring of rational homogeneous varieties of classical type, more concretely, effective zero divisors of low codimension, and a related invariant called effective good divisibility. This…

We introduce two new homology theories of orbifolds from some special type of triangulations adapted to an orbifold, called AW-homology and DW-homology. The main idea in the definitions of these two homology theories is that we use…

Starting from the axiomatic description of meromorphic functions with prescribed analytic properties, we introduce the cosimplicial cohomology of restricted meromorphic functions defined on foliations of smooth complex manifolds. Spaces for…

In this note, we give a motivic characterization of the integral cohomology of dual boundary complexes of smooth quasi-projective complex algebraic varieties. As a corollary, the dual boundary complex of any stably affine space (of positive…

Let $G$ be a semi-simple algebraic group over a perfect field $k$. A lot of progress has been made recently in computing the Chow motives of projective $G$-homogenous varieties. When $k$ has positive characteristic, a broader class of…

Given a sheaf on a projective space P^n we define a sequence of canonical and easily computable Chow complexes on the Grassmannians of planes in P^n, generalizing the Beilinson monad on P^n. If the sheaf has dimension k, then the Chow form…

We compute the stringy chow ring of a general Deligne-Mumford stack of the form [X/G] for a smooth variety X and diagonalizable group scheme G, working over a base field that is not necessarily algebraically closed. We then specialize to…

We explain how complexity of rational points on projective varieties can be interpreted via the theories of Chow forms and Okounkov bodies. Precisely, we study discrete measures on filtered linear series and build on work of Boucksom and…