Related papers: Framed motivic $\Gamma$-spaces

We present a geometric construction of push-forward maps along projective morphisms for cohomology theories representable in the stable motivic homotopy category assuming that the element corresponding to the stable Hopf map is inverted in…

In this paper, we initiate a study of motivic homotopy theory at infinity. We use the six functor formalism to give an intrinsic definition of the stable motivic homotopy type at infinity of an algebraic variety. Our main computational…

We construct models for the motivic homotopy category based on simplicial functors from smooth schemes over a field to simplicial sets. These spaces are homotopy invariant and therefore one does not have to invert the affine line in order…

Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…

We develop algebraic geometry for general Segal's Gamma-rings and show that this new theory unifies two approaches we had considered earlier on (for a geometry under Spec Z). The starting observation is that the category obtained by gluing…

In this paper, we introduce the notions of motivic representation stability that is an algebraic counterpart of the notion of representation stability. In the process, we also introduce the notion of motivic decomposition for varieties…

(This is an updated version; following an idea of Voevodsky, we have strengthened our results so all of them apply to one form of motivic homotopy theory). We give two general constructions for the passage from unstable to stable homotopy…

Generalising Segal's approach to 1-fold loop spaces, the homotopy theory of $n$-fold loop spaces is shown to be equivalent to the homotopy theory of reduced $\Theta_n$-spaces, where $\Theta_n$ is an iterated wreath product of the simplex…

We provide a gentle introduction to arc spaces, motivic integration and stringy invariants. We explain the basic concepts and first results, including the p-adic number theoretic pre-history, and we provide concrete examples. The text is a…

We develop a framework based on the covariant phase space formalism that identifies gravitational edge modes as dynamical reference frames. They enable the identification of the associated spacetime region and the imposition of boundary…

In this work we develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. Our construction is based on the notion of finite log correspondences, the dividing Nisnevich topology on log…

We prove the geometric Satake equivalence for mixed Tate motives over the integral motivic cohomology spectrum. This refines previous versions of the geometric Satake equivalence for split reductive groups. Our new geometric results include…

We consider a class of graphs subject to certain restrictions, including the finiteness of diameters. Any surjective mapping $\phi:\Gamma\to\Gamma'$ between graphs from this class is shown to be an isomorphism provided that the following…

We define a trace map for every cohomological correspondence in the motivic stable homotopy category over a general base scheme, which takes values in the twisted bivariant groups. Local contributions to the trace map give rise to quadratic…

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.

We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…

In the present article we study the following problem. Let G be a linear algebraic group over Q, $\Gamma$ be an arithmetic lattice and H be an observable Q-subgroup. There is a H-invariant measure $\mu_H$ supported on the closed submanifold…

The goal of this paper is to study non-$\mathbb{A}^1$-invariant motivic cohomology, recently defined by Elmanto, Morrow, and the first-named author, for smooth schemes over possibly non-discrete valuation rings. We establish that the cycle…

We categorify the inclusion-exclusion principle for partially ordered topological spaces and schemes to a filtration on the derived category of sheaves. As a consequence, we obtain functorial spectral sequences that generalize the two…

We reformulate the construction of Kontsevich's completion and use Lawson homology to define many new motivic invariants. We show that the dimensions of subspaces generated by algebraic cycles of the cohomology groups of two $K$-equivalent…