Related papers: Real isotropic motivic spectra
Our main purpose is to describe the category of isotropic cellular spectra over flexible fields. Guided by [6], we show that it is equivalent, as a stable $\infty$-category equipped with a $t$-structure, to the derived category of left…
The main goal of this paper is to study relative versions of the category of modules over the isotropic motivic Brown-Peterson spectrum, with a particular emphasis on their cellular subcategories. Using techniques developed by Levine, we…
In this paper, we produce a cellular motivic spectrum of motivic modular forms over $\R$ and $\C$, answering positively to a conjecture of Dan Isaksen. This spectrum is constructed to have the appropriate cohomology, as a module over the…
To an Adams-type homology theory we associate a notion of a synthetic spectrum, this is a product-preserving sheaf on the site of finite spectra with projective $E$-homology. We prove that the $\infty$-category $Syn_{E}$ of synthetic…
Let k be an algebraically closed field of characteristic zero. Let SH(k) denote the motivic stable homotopy category of T-spectra over k and SH the classical stable homotopy category. Let c:SH -> SH(k) be the functor induced by sending a…
We exhibit a relationship between motivic homotopy theory and spectral algebraic geometry, based on the motivic $\tau$-deformation picture of Gheorghe, Isaksen, Wang, Xu. More precisely, we identify cellular motivic spectra over $\mathbf C$…
We prove a motivic version of Landweber's exact functor theorem from topology. The main result is that the assignment given by a Landweber-type formula using the MGL-homology of a motivic spectrum defines a homology theory on the stable…
In this paper we explore the isotropic stable motivic homotopy category constructed from the usual stable motivic homotopy category, following the work of Vishik on isotropic motives (see [29]), by killing anisotropic varieties. In…
We give a method for computing the C_2-equivariant homotopy groups of the Betti realization of a p-complete cellular motivic spectrum over R in terms of its motivic homotopy groups. More generally, we show that Betti realization presents…
Working over an algebraically closed field $k$ of characteristic $0$, we show that the motivic stable homotopy groups of the sphere spectrum can be determined entirely from the motivic homotopy groups of the $p$-completed sphere spectra and…
Real Betti realization is a symmetric monoidal functor from the category of motivic spectra to that of topological spectra, extending the functor that associates to a scheme over $\mathbb{R}$ the space of its real points. In this article,…
We prove a topological reconstruction result for the category of cellular $A$-equivariant motivic spectra over the complex numbers where $A$ is a finite abelian group: after completion at an arbitrary prime, this is equivalent to the…
We prove that the $\infty$-category of motivic spectra satisfies Milnor excision: if $A\to B$ is a morphism of commutative rings sending an ideal $I\subset A$ isomorphically onto an ideal of $B$, then a motivic spectrum over $A$ is…
We study liftings of abelian model structures to categories of chain complexes and construct a realization functor from the derived category of a Grothendieck abelian category equipped with a cofibrantly generated, hereditary abelian model…
We define real topological Hochschild homology of separated log schemes with involutions. We show that real topological Hochschild homology is $(\mathbb{P}^n,\mathbb{P}^{n-1})$-invariant, which leads to the definition of the motivic real…
We give, for a complex algebraic variety $S$, a Hodge realization functor $\mathcal F_S^{Hdg}$ from the derived category of constructible motives $DA_c(S)$ to the derived category $D(MHM(S))$ of algebraic mixed Hodge modules over $S$.…
We formalize an abstraction of Grothendieck's philosophy of motives and construct a category of derived motivic spectra in the Segal category $\mathbb{R} \underline{\text{Hom}} ((\text{dSt}_k)^{\text{op}}_{/F}, \text{Top})$ ($\text{dSt}_k$…
We reconstruct (appropriately completed) categories of cellular motivic spectra over fields of small cohomological dimension in terms of only their absolute Galois groups. As our main application, we determine the motivic stable stems (away…
An object in motivic homotopy theory is called cellular if it can be built out of motivic spheres using homotopy colimit constructions. We explore some examples and consequences of cellularity. We explain why the algebraic K-theory and…
We provide a description of Voevodsky's $\infty$-category of motivic spectra in terms of the subcategory of motives of smooth proper varieties. As applications, we construct weight filtrations on the Betti and \'{e}tale cohomologies of…