Related papers: Motivic rational homotopy type
The aim of this paper is to introduce a mathematical logic based approach investigating why-type questions in physics.
The purpose of this article is to clarify the question what makes motives $\mathbb{A}^1$-homotopy invariance. we give construction of the stable model category of nilpotent invariant motives…
We compute the 2-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of motivic cohomology and hermitian K-groups.
The proof of the coincidence of the Gysin morphism in motivic cohomology and the usual pushout on Chow groups has been improved (see Lemma 3.3 and Proposition 3.11)
This expository paper is concerned with the rationality problems for three-dimensional algebraic varieties with a conic bundle structure. We discuss the main methods of this theory. We sketch the proofs of certain principal results, and…
We introduce and study matrix transfers to achieve elementary models for bivariant $K$-theory. They share lots of common properties with Voevodsky's framed correspondences and lead to symmetric matrix motives of algebraic varieties…
We provide explicit equations and parameterizations of some new rational Gushel-Mukai fourfolds of special type.
We classify the possible Mumford-Tate groups of polarizable rational Hodge structures. Along the way we deduce a polarized Hodge-theoretic analogue of a conjectural property of motivic Galois groups suggested by Serre.
In this paper we describe the category of motives for an elliptic curve in the sense of Voevodsky as a derived category of dg modules over a commutative differential graded algebra in the category of representations over some reductive…
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
Hypergeometric motives are family of motives associated to hypergeometric local systems. Their special features, in particular their rigidity, makes them more tractable than general motives. In the present article we prove most of the…
This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.
We survey recent work on moduli spaces of manifolds with an emphasis on the role played by (stable and unstable) homotopy theory. The theory is illustrated with several worked examples.
We give a short constructive proof for the existence and uniqueness of the rational normal form of a quadratic matrix.
This technical report investigates Kripke-style modal type theories, both simply typed and dependently typed. We examine basic meta-theories of the type theories, develop their substitution calculi, and give normalization by evaluation…
We prove that some of the classical homological stability results for configuration spaces of points in manifolds can be lifted to motivic cohomology.
We compute the set of naive pointed homotopy classes of endomorphisms of the projective line P^1 over the spectrum of a field. Our computation compares well with Fabien Morel's one of the motivic pointed homotopy classes of endomorphisms of…
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
Let $G$ be a reductive group over $\mathbb{F}_{p}$ with associated finite group of Lie type $G^{F}$. Let $T$ be a maximal torus contained inside a Borel $B$ of $G$. We relate the (rational) Tate motives of $\text{B}G^{F}$ with the…
Let A be a subspace arrangement with a geometric lattice such that codim(x) > 1 for every x in A. Using rational homotopy theory, we prove that the complement M(A) is rationally elliptic if and only if the sum of the orthogonal subspaces is…