Related papers: Framed and MW-transfers for homotopy modules

This work is dedicated to the construction of a new motivic homotopy theory for (log) schemes, generalizing Morel-Voevodsky's (un)stable $\mathbb{A}^1$-homotopy category. Our framework can be used to represent log topological Hochschild and…

We study the category $DM(S)$ of Beilinson motives (as described by Cisinski and Deglise) over a more or less general base scheme $S$, and establish several nice properties for a version $t_{hom}(S)$ of the perverse homotopy $t$-structure…

We show that mapping spaces in the p-local motivic stable category over an Fp-scheme are strictly commutative monoids (whence HZ-modules) in a canonical way.

This dissertation comprises three collections of results, all united by a common theme. The theme is the study of categories via algebraic techniques, considering categories themselves as algebraic objects. This algebraic approach to…

We show that an A-infinity algebra structure can be transferred to a projective resolution of the complex underlying any A-infinity algebra. Under certain connectedness assumptions, this transferred structure is unique up to homotopy. In…

In this short note, we argue that directed homotopy can be given the structure of generalized modules, over particular monoids. This is part of a general attempt for refoundation of directed topology.

Let X be a Noetherian scheme of finite dimension and denote by rho the (additive inverse of the) morphism in SH(X) from S to Gm corresponding to the unit -1. Here SH(X) denotes the motivic stable homotopy category. We show that the category…

If $f:S' \to S$ is a finite locally free morphism of schemes, we construct a symmetric monoidal "norm" functor $f_\otimes: \mathcal H_*(S') \to\mathcal H_*(S)$, where $\mathcal H_*(S)$ is the pointed unstable motivic homotopy category over…

We generalize several basic facts about the motivic sphere spectrum in $\mathbb A^1$-homotopy theory to the category $\mathrm{MS}$ of non-$\mathbb A^1$-invariant motivic spectra over a derived scheme. On the one hand, we show that all the…

For each prime $p$, we define a $t$-structure on the category $\widehat{S^{0,0}}/\tau\text{-}\mathbf{Mod}_{harm}^b$ of harmonic $\mathbb{C}$-motivic left module spectra over $\widehat{S^{0,0}}/\tau$, whose MGL-homology has bounded…

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in any triangulated category D with arbitrary (set-indexed) coproducts. We show that equivalence classes of partial silting sets are in bijection…

Smooth projective $\mathbb{G}_m$-varieties with isolated rational fixed points admit Tate Milnor-Witt motives. Over Euclidean fields, we give a splitting formula of such motives, which reduces the computation of their Chow-Witt groups to…

We prove that for a finitely generated field over an infinite perfect field k, and for any integer n, the (n,n)-th MW-motivic cohomology group identifies with the n-th Milnor-Witt K-theory group of that field

We show that finite Milnor-Witt correspondences satisfy a cancellation theorem with respect to the pointed multiplicative group scheme. This has several notable applications in the theory of Milnor-Witt motives and Milnor-Witt motivic…

Given an algebraic stack $X$, one may compare the derived category of quasi-coherent sheaves on $X$ with the category of dg-modules over the dg-ring of functions on $X$. We study the analogous question in stable homotopy theory, for derived…

We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…

Transfer systems on finite posets have recently been gaining traction as a key ingredient in equivariant homotopy theory. Additionally, they also naturally occur in the data of a model structure. We give a complete characterization of all…

This article computes some motivic stable homotopy groups over R. For 0 <= p - q <= 3, we describe the motivic stable homotopy groups of a completion of the motivic sphere spectrum. These are the first four Milnor-Witt stems. We start with…

We constructed the analytic Milnor fiber is a non-archimedean model of the classical topological Milnor fibration. In the present paper, we describe the homotopy type of the analytic Milnor fiber in terms of a strictly semi-stable model,…

Let $M$ be a smooth manifold. We use Chern-Weil theory to study the characteristic classes of principal $G$-bundles built from continuous families of $\pi_{1}(M)$-representations, where $G$ is a compact Lie group. We then relate these…