Related papers: Motivic characteristic classes

Let X be a smooth, complete, toric variety. We study those curves C in X that are contractible, in the sense that there exists an equivariant morphism with connected fibers, with source X, that contracts exactly the irreducible curves that…

Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value…

We study hyperbolic cohomology classes in the general context of simplicial complexes and prove homological invariance statements for them. We relate the existence of hyperbolic cohomology classes to the non-amenability of the fundamental…

In this paper we prove that the motivic Eisenstein classes associated to polylogarithms of commutative group schemes can be $p$-adically interpolated in \'etale cohomology. This generalizes results for elliptic curves obtained in our former…

A Q-manifold is a graded manifold endowed with a vector field of degree one squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of ``gauge fields'' (sections…

We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…

We associate canonical virtual motives to definable sets over a field of characteristic zero. We use this construction to show that very general p-adic integrals are canonically interpolated by motivic ones.

Although the characterization of ring derivations has an extensive literature, up to now, all of the characterizations have had the following form: additivity and another property imply that the function in question is a derivation. The aim…

Grothendieck-Chow motives of quadric hypersurfaces have provided many insights into the theory of quadratic forms. Subsequently, the landscape of motives of more general projective homogeneous varieties has begun to emerge. In particular,…

We explain and explore class-theoretic potentialism -- the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning…

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…

Magnitude homology is an invariant of enriched categories which generalizes ordinary categorical homology -- the homology of the classifying space of a small category. The classifying space can also be generalized in a different direction:…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

We prove the conjectured compatibility of $p$-adic fundamental lines with specializations at motivic points for a wide class of $p$-adic families of $p$-adic Galois representations (for instance, the families which arise from $p$-adic…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

Let $k$ be a field, let $R$ be a commutative ring, and assume the exponential characteristic of $k$ is invertible in $R$. In this note, we prove that isomorphisms in Voevodsky's triangulated category of motives $\mathcal{DM}(k;R)$ are…

In this note, we prove that intrinsic characteristic classes of Lie algebroids - which in degree one recover the modular class - behave functorially with respect to arbitrary transverse maps, and in particular are weak Morita invariants. In…

We classify all finite-dimensional connected Hopf algebras with large abelian primitive spaces. We show that they are Hopf algebra extensions of restricted enveloping algebras of certain restricted Lie algebras. For any abelian matched pair…

Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…

We survey some topics in ${\mathbb A}^1$-homotopy theory. Our main goal is to highlight the interplay between ${\mathbb A}^1$-homotopy theory and affine algebraic geometry, focusing on the varieties that are "contractible" from various…