Related papers: Motivic intersection complex

We find explicit formulas for the Hilbert series of residual intersections of a scheme in terms of the Hilbert series of its conormal modules. In a previous paper we proved that such formulas should exist. We give applications to the…

We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines $\Gamma$-spaces and framed…

We develop a theory of modulus triples, for future motivic applications.

The intersection matrix of a finite simplicial complex has as each of its entries the rank of the intersection of its respective simplices. We prove that such matrix defines the triangulation of a closed connected surface up to isomorphism.

We use the theory of motivic integration in order to give a geometric explanation of the behavior of some p-adic integrals.

Addressing a question of Zaremsky, we give conditions on a finite simplicial graph which guarantee that the associated matching arc complex is connected and hyperbolic.

We study the logic of neighbourhood models with pointwise intersection, as a means to characterize multi-modal logics. Pointwise intersection takes us from a set of neighbourhood sets $\mathcal{N}_i$ (one for each member $i$ of a set $G$,…

In this article, we construct a Hecke-equivariant Chow motive whose realizations equal intersection cohomology of Siegel threefolds with regular algebraic coefficients. As a consequence, we are able to define Grothendieck motives for Siegel…

This article gives an introduction to arithmetic motivic integration in the context of p-adic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives.

Two semisimple algebraic groups of the same type are said to be motivic equivalent if the motives of the associated projective homogeneous varieties of the same type are isomorphic. We give general criteria of motivic equivalence in terms…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.

We show that the detection of geometric intersection in an arbitrary representation of the mapping class group of surface implies the injectivity of that representation up to center, and vice versa. As an application, we discuss the…

In this paper, we study the combinatorics of a subcomplex of the Bloch-Kriz cycle complex [4] used to construct the category of mixed Tate motives. The algebraic cycles we consider properly contain the subalgebra of cycles that correspond…

Several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded $k$-algebra; these notions are justified by examples from noncommutative invariant theory.

We prove a recognition principle for motivic infinite P1-loop spaces over a perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of the theory of E-infinity-spaces. A framed motivic…

We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…

We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among…

This is a short announcement and summary of the results of arxiv:1111.7057, arxiv.org:1111.4405, and Appendix B to arxiv:1208.1945. In particular, we emphasize the exposition of the ideas related to model theory and motivic integration, and…

We construct Toda brackets in unstable motivic homotopy theory and prove some fundamental properties of them. Furthermore we construct some examples of motivic Toda brackets.