Related papers: Cousin complexes in motivic homotopy theory

We study the homotopy groups of complements to reducible divisors on non-singular projective varieties with ample components and isolated non normal crossings. We prove a vanishing theorem generalizing conditions for commutativity of the…

This document contains large-format Adams charts that compute 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. The charts are essentially complete through the 61-stem and contain partial…

We solve a motivic version of the Adams conjecture with the exponential characteristic of the base field inverted. In the way of the proof we obtain a motivic version of mod k Dold theorem and give a motivic version of Brown's trick…

We study the homotopy theory of a certain type of diagram categories whose vertices are in variable categories with a functorial path, leading to a good calculation of the homotopy category in terms of cofibrant objects. The theory is…

Fix the base field Q of rational numbers and let BP<n> denote the family of motivic truncated Brown-Peterson spectra over Q. We employ a "local-to-global" philosophy in order to compute the motivic Adams spectral sequence converging to the…

This paper is the second one in a series of papers about operations in motivic cohomology. Here we show that in the context of smooth schemes over a field of characteristic zero all the bi-stable operations can be obtained in the usual way…

We introduce (co)homology theory for multiple group racks and construct cocycle invariants of compact oriented surfaces in the 3-sphere using their 2-cocycles, where a multiple group rack is a rack consisting of a disjoint union of groups.…

In this paper we show that Bloch's higher cycle class map with finite coefficients for quasi-projective equi-dimensional schemes over a field fits naturally in a long exact sequence involving Schreieder's refined unramified cohomology. We…

We show that coorbit spaces can be characterized in terms of arbitrary phase-space covers, which are families of phase-space multipliers associated with partitions of unity. This generalizes previously known results for time-frequency…

The topic of this thesis is the application of distributive laws between comonads to the theory of cyclic homology. Explicitly, our main aims are: 1) To study how the cyclic homology of associative algebras and of Hopf algebras in the…

Over the complex numbers, we compute the $C_2$-equivariant Bredon motivic cohomology ring with $\mathbb{Z}/2$ coefficients. By rigidity, this extends Suslin's calculation of the motivic cohomology ring of algebraically closed fields of…

Let G be a split, simple, simply connected, algebraic group over Q. The degree 4, weight 2 motivic cohomology group of the classifying space BG of G is identified with Z. We construct cocycles representing the generator of this group, known…

We use assembly maps to study $\mathbf{TC}(\mathbb{A}[G];p)$, the topological cyclic homology at a prime $p$ of the group algebra of a discrete group $G$ with coefficients in a connective ring spectrum $\mathbb{A}$. For any finite group, we…

In this paper we suggest a definition for the category of mixed motives generated by the motive h^1(E) for E an elliptic curve without complex multiplication. We then compute the cohomology of this category. Modulo a strengthening of the…

We study in detail the so-called Chow-weight homology of Voevodsky motivic complexes and relate it to motivic homology. We generalize earlier results and prove that the vanishing of higher motivic homology groups of a motif $M$ implies…

We define a motivic Greenlees spectral sequence by characterising an associated $t$-structure. We then examine a motivic version of topological Hochschild homology for the motivic cohomology spectrum modulo a prime number $p$. Finally, we…

We study quotients of quasi-affine schemes by unipotent groups over fields of characteristic 0. To do this, we introduce a notion of stability which allows us to characterize exactly when a principal bundle quotient exists and, together…

We establish a loop space decomposition for certain $CW$-complexes with a single top cell in the presence of a spherical pair, thereby generalizing several known decompositions of Poincar\'{e} duality complexes in which a loop of a product…

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…

Piecewise-linear maps describe dynamical phenomena that switch between distinct states and readily generate complex bifurcation structures due to their strong nonlinearity. We show that two-dimensional continuous piecewise-linear maps near…