Related papers: On equivariant and motivic slices

We study the equivalence between bipartiteness and symmetry of spectra of mixed graphs, for $\theta$-Hermitian adjacency matrices defined by an angle $\theta \in (0, \pi]$. We show that this equivalence holds when, for example, an angle…

Let $\mathfrak{g}$ be a semisimple Lie algebra, $\mathfrak{t}$ its Cartan subalgebra and $W$ the Weyl group. The goal of this paper is to prove an isomorphism between suitable completions of the equivariant Borel-Moore homology of certain…

We construct a motivic spectral sequence for the relative homotopy invariant K-theory of a closed immersion of schemes $D \subset X$. The $E_2$-terms of this spectral sequence are the cdh-hypercohomology of a complex of equi-dimensional…

Given an E-infinity ring spectrum R, with motivation from chromatic homotopy theory, we define relative effective Cartier divisors for a spectral Deligne-Mumford stack over Spet(R) and prove that, as a functor from connective R-algebras to…

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…

Let $R$ be a perfectoid ring. Hesselholt and Bhatt-Morrow-Scholze have identified the Postnikov filtration on $\mathrm{THH}(R;\mathbb Z_p)$: it is concentrated in even degrees, generated by powers of the B\"okstedt generator $\sigma$,…

The aim of this paper is to connect two important and apparently unrelated theories: motivic homotopy theory and ramification theory. We construct motivic homotopy categories over a qcqs base scheme $S$, in which cohomology theories with…

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 compute the motivic Milnor fiber of a complex plane curve singularity in an inductive and combinatoric way using the extended simplified resolution graph. The method introduced in this article has a consequence that one can study the…

Let h \subset g be an inclusion of Lie algebras with quotient h-module n. There is a natural degree filtration on the h-module U(g)/U(g)h whose associated graded h-module is isomorphic to S(n). We give a necessary and sufficient condition…

For a finite Galois extension of fields L/k with Galois group G, we study a functor from the G-equivariant stable homotopy category to the stable motivic homotopy category over k induced by the classical Galois correspondence. We show that…

We show that the motivic spectrum representing algebraic $K$-theory is a localization of the suspension spectrum of $\mathbb{P}^\infty$, and similarly that the motivic spectrum representing periodic algebraic cobordism is a localization of…

This paper sets up the foundations for derived algebraic geometry, Goerss--Hopkins obstruction theory, and the construction of commutative ring spectra in the abstract setting of operadic algebras in symmetric spectra in an (essentially)…

We obtain conditions for a trigonometric polynomial t of one variable to equal or be approximated by |p|^2 where p has frequencies in a Bohr set of integers obtained by projecting lattice points in the open planar region bounded by the…

We prove the analog of the Morel-Voevodsky localization theorem for framed motivic spaces. We deduce that framed motivic spectra are equivalent to motivic spectra over arbitrary schemes, and we give a new construction of the motivic…

In this paper we prove over fields of characteristic zero that the zero slice of the motivic sphere spectrum is the motivic Eilenberg-Maclane spectrum. As a corollary one concludes that the slices of any spectrum are modules over the…

We show that the restriction to a smooth transversal section commutes to the computation of multiplier ideals and V-filtrations. As an application we prove the constancy of the spectrum along any stratum of a Whitney regular stratification.

We make some computations in stable motivic homotopy theory over Spec \mathbb{C}, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct a motivic analogue of the real K-theory spectrum KO. We also…

A Thom spectrum model for a $C_2$-equivariant analogue of integral Brown--Gitler spectra is established and shown to have a multiplicative property. The $C_2$-equivariant spectra constructed enjoy properties analogous to classical…

We explore the $C_2$-equivariant spectra $Tmf_1(3)$ and $TMF_1(3)$. In particular, we compute their $C_2$-equivariant Picard groups and the $C_2$-equivariant Anderson dual of $Tmf_1(3)$. This implies corresponding results for the fixed…