Related papers: Motivic intersection complex

Motivic characteristic classes of possibly singular algebraic varieties are homology class versions of motivic characteristics, not classes in the so-called motivic (co)homology. This paper is a survey on them with more emphasis on…

We prove a motivic enhancement of the classical Picard--Lefschetz formula. Our proof is completely motivic, and yields a description of the motivic nearby cycles at a quasi-homogeneous singularity, as well as its monodromy, in terms of an…

We prove the complete intersection theorem and complete nontrivial-intersection theorem for systems of set partitions

We investigate various homotopy invariant formulations of commutative algebra in the context of rational homotopy theory. The main subject is the complete intersection condition, where we show that a growth condition implies a structure…

Already in the 1960s Grothendieck understood that one could obtain an almost entirely satisfactory theory of motives over a finite field when one assumes the full Tate conjecture. In this note we prove a similar result for motivic…

The intersection type assignment system has been designed directly as deductive system for assigning formulae of the implicative and conjunctive fragment of the intuitionistic logic to terms of lambda-calculus. But its relation with the…

We define a variant of intersection space theory that applies to many compact complex and real analytic spaces $X$, including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to…

For a split reductive group G over a finite field, we show that the intersection (cohomology) motive of the moduli stack of iterated G-shtukas with bounded modification and level structure is defined independently of the standard…

The aim of this article is to develop the theory of motivic integration over Deligne-Mumford stacks and to apply it to the birational geometry of stacks.

We determine the structure of the finite groups with the property that every cyclic subgroup is the intersection of maximal subgroups, comparing this property with the one where all proper subgroups are intersections of maximal subgroups.

In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes from directed graphs(digraphs). We obtain a new notion of the…

In this article, we study the question of existence of leafwise intersection points for contact manifolds which are not necessarily of restricted contact type. Moreover we can find a leafwise intersection point on the symplectization for…

We introduce the notion of residual intersections of modules and prove their existence. We show that projective dimension one modules have Cohen-Macaulay residual intersections, namely they satisfy the relevant Artin-Nagata property. We…

We define a simpler notion of symmetric topological complexity more ad hoc to the motion planning problem which was the original motivation for the definition of topological complexity. This is a homotopy invariant that we call…

We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…

This note addresses the motivic nature of some classical cohomological results due to Lefschetz, namely the primitive decomposition (for the cohomology of smooth projective varieties), and, secondly, the splitting of the cohomology of a…

Assuming the K\"unneth type standard conjecture, we propose a way to describe objects of mixed motives explicitly. We study their formal properties, and we associate mixed motives to schemes smooth and separated over a field. This serves as…

Intersection types are an essential tool in the analysis of operational and denotational properties of lambda-terms and functional programs. Among them, non-idempotent intersection types provide precise quantitative information about the…

Using punctual gluing of $t$-structures, we construct an analogue of S. Morel's weight truncation functors (for certain weight profiles) in the setting of motivic sheaves. As an application we construct a canonical motivic analogue of the…

We give a presentation of the motivic cohomology ring of the complement of a hyperplane arrangement considered as algebra over the motivic cohomology of the ground field.