Related papers: Motivic rational homotopy type

We give an introduction to unstable motivic homotopy theory of Morel and Voevodsky, and survey some results.

We compute the $v_1$-periodic $\mathbb{R}$-motivic stable homotopy groups. The main tool is the effective slice spectral sequence. Along the way, we also analyze $\mathbb{C}$-motivic and $\eta$-periodic $v_1$-periodic homotopy from the same…

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.

Motivated by a problem in motivic homotopy theory considered by Asok-Fasel-Hopkins, we give a description of the rational $C_2$-equivariant homotopy type of the classifying space ${BSU_{\mathbb{R}}}_m$ in terms of equivariant…

This paper defines homology in homotopy type theory, in the process stable homotopy groups are also defined. Previous research in synthetic homotopy theory is relied on, in particular the definition of cohomology. This work lays the…

Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for…

We study the structure of the rational motivic stable homotopy category over general base schemes. Our first class of results concerns the six operations: we prove absolute purity, stability of constructible objects, and…

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

We prove a comparison isomorphism between the De Rham rational homotopy type of a smooth proper log variety defined over a p-adic field and the crystalline rational homotopy type of a semi-stable reduction mod p.

We develop the theory of motivic integration for formal schemes

We show that the category of log homotopy types is a full subcategory of a category of homotopy types with modulus.

We construct more non-trivial examples for Toda brackets in unstable motivic homotopy theory via the first and second motivic Hopf maps.

This paper aims to help the development of new models of homotopy type theory, in particular with models that are based on realizability toposes. For this purpose it develops the foundations of an internal simplicial homotopy that does not…

Homotopy Type Theory is a new field of mathematics based on the surprising and elegant correspondence between Martin-Lofs constructive type theory and abstract homotopy theory. We have a powerful interplay between these disciplines - we can…

In this expository article, we give the foundations, basic facts, and first examples of unstable motivic homotopy theory with a view towards the approach of Asok-Fasel to the classification of vector bundles on smooth complex affine…

We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.

In the rational cohomology of a 1-connected space a structure of $C_{\infty}$-algebra is constructed and it is shown that this object determines the rational homotopy type

We strengthen some results in \'etale (and real \'etale) motivic stable homotopy theory, by eliminating finiteness hypotheses, additional localizations and/or extending to spectra from HZ-modules.

In this article, we give an unconditional definition of the motivic analogue of the intersection complex, establish its basic properties, and prove its existence in certain cases.

We discuss some examples of geometrically meaningful rational self-maps of moduli space of curves of low genus and homogeneous forms.