Related papers: Motivic Landweber Exactness
Already in the 1960s Grothendieck understood that one could obtain an almost entirely satisfactory theory of motives over a finite field when one assumes the full Tate conjecture. In this note we prove a similar result for motivic…
Spectral Mackey functors are homotopy-coherent versions of ordinary Mackey functors as defined by Dress. We show that they can be described as excisive functors on a suitable infinity-category, and we use this to show that universal…
We construct a theory of motivic cohomology for quasi-compact, quasi-separated schemes of equal characteristic, which is related to non-connective algebraic $K$-theory via an Atiyah--Hirzebruch spectral sequence, and to \'etale cohomology…
We prove that the $\infty$-category of $\mathrm{MGL}$-modules over any scheme is equivalent to the $\infty$-category of motivic spectra with finite syntomic transfers. Using the recognition principle for infinite $\mathbb{P}^1$-loop spaces,…
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,…
We formalize an abstraction of Grothendieck's philosophy of motives and construct a category of derived motivic spectra in the Segal category $\mathbb{R} \underline{\text{Hom}} ((\text{dSt}_k)^{\text{op}}_{/F}, \text{Top})$ ($\text{dSt}_k$…
Let $G$ be a linear semisimple algebraic group and $B$ its Borel subgroup. Let $\mathbb{T}\subset B$ be the maximal torus. We study the inductive construction of Bott-Samelson varieties to obtain recursive formulas for the twisted motivic…
Assuming the Hodge conjecture for abelian varieties of CM-type, one obtains a good category of abelian motives over the algebraic closure of a finite field and a reduction functor to it from the category of CM-motives. Consequentely, one…
We propose a motivic version of T. Hausel and M. Thaddeus' Topological Mirror Symmetry for character stacks associated with arbitrary semisimple groups, which is an analogue of F. Loeser and D. Wyss' result for Chow motives of moduli spaces…
We use motivic colimits to construct power operations on the homotopy groups of normed motivic spectra admitting a (normed) map from HF_2. We establish enough of their standard properties to prove that the motivic dual Steenrod algebra is…
We construct a 'triangulated analogue' of coniveau spectral sequences: the motif of a variety over a countable field is 'decomposed' (in the sense of Postnikov towers) into the twisted (co)motives of its points; this is generalized to…
Thomason's \'{e}tale descent theorem for Bott periodic algebraic $K$-theory \cite{aktec} is generalized to any $MGL$ module over a regular Noetherian scheme of finite dimension. Over arbitrary Noetherian schemes of finite dimension, this…
In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…
A map between manifolds induces stratifications of both the source and the target according to the occurring multisingularities. In this paper, we study universal expressions-called higher Thom polynomials-that describe the…
We prove a bijective unitary correspondence between 1) the isospectral torus of almost-periodic, absolutely continuous CMV matrices having fixed finite-gap spectrum and 2) special periodic block-CMV matrices satisfying a Magic Formula. This…
We prove that every functor defined on dg categories, which is derived Morita invariant, localizing, and A^1-homotopy invariant, satisfies the fundamental theorem. As an application, we recover in a unified and conceptual way, Weibel and…
In joint work with Elmanto, Hoyois, Khan and Sosnilo, we computed infinite $\mathbb{P}^1$-loop spaces of motivic Thom spectra, using the technique of framed correspondences. This result allows us to express non-negative…
We define Hodge correlators for a compact Kahler manifold X. They are complex numbers which can be obtained by perturbative series expansion of a certain Feynman integral which we assign to X. We show that they define a functorial real…
We analyze the $\mathbb{C}$-motivic (and classical) Adams-Novikov spectral sequence for the $\mathbb{C}$-motivic modular forms spectrum $\mathit{mmf}$ (and for the classical topological modular forms spectrum $\mathit{tmf}$). We primarily…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…