Related papers: Subtle characteristic classes for $Spin$-torsors

In this article, we study the rational cohomology rings of Voisin's punctual Hilbert schemes $X^{[n]}$ associated to a symplectic compact fourfold $X$. We prove that these rings can be universally constructed from $H^*(X,\mathbb{Q})$ and…

The quadric $\operatorname{Q}_{2n}$ is the ${\mathbb Z}$-scheme defined by the equation $\sum_{i=1}^n x_i y_i = z(1-z)$. We show that $\operatorname{Q}_{2n}$ is a homogeneous space for the split reductive group scheme…

We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main additional ingredient is an extension of the Eells-Kuiper…

These notes accompany a lecture about the topology of symplectic (and other) quotients. The aim is two-fold: first to advertise the ease of computation in the symplectic category; and second to give an account of some new computations for…

The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group over a regular semilocal ring is itself trivial. Extending the work of \v{C}esnavi\v{c}ius and Fedorov, we prove a non-noetherian…

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 generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi-projective variety. More concretely, we study homology Hirzebruch classes for motivic coefficients, as well as…

The motivic homotopy categories can be defined with respect to different topologies and different underlying categories of schemes. For a number of reasons (mainly because of the Gluing Theorem) the motivic homotopy category built out of…

We examine the integral cohomology rings of certain families of $2n$-dimensional orbifolds $X$ that are equipped with a well-behaved action of the $n$-dimensional real torus. These orbifolds arise from two distinct but closely related…

We introduce a spherical variant of Milnor's classifying construction for diffeological groups, based on quadratic normalization of barycentric coordinates. This construction gives rise to a contractible diffeological space endowed with…

In this note we give a geometric realization of the cohomology of Springer fibers in type A. More precisely, we describe the cohomology by the coordinate ring of a scheme theoretic intersection of a Cartan subalgebra with a certain union of…

For each integer $d$ at least two, we construct non-spin closed oriented flat manifolds with holonomy group $\mathbb Z_2^d$ and with the property that all of their finite proper covers have a spin structure. Moreover, all such covers have…

We prove that the Chow motives of twisted derived equivalent K3 surfaces are isomorphic, not only as Chow motives (due to Huybrechts), but also as Frobenius algebra objects. Combined with a recent result of Huybrechts, we conclude that two…

For any cohomology theory $H$ that can be factorized through (the Morel-Voevodsky's triangulated motivic homotopy category) $SH^{S^1}(k)$ we establish the $SH^{S^1}(k)$-functoriality of coniveau spectral sequences for $H$. We also prove:…

To smooth schemes equipped with a smooth affine group scheme action, we associate an equivariant motivic homotopy category. Underlying our construction is the choice of an `equivariant Nisnevich topology' induced by a complete, regular, and…

For the split group $G_{2}$ defined over $\mathbb{Z},$ we show that the de Rham cohomology ring of $B(G_{2})_{\mathbb{F}_{2}}$ is isomorphic to the singular cohomology ring with $\mathbb{F}_{2}$-coefficients of $B(G_{2})_{\mathbb{C}}.$ For…

Combining work of Peyre, Colliot-Th\'el\`ene and Voisin, we give the first example of a finite group $G$ such that the motivic class of its classifying stack $BG$ in Ekedahl's Grothendieck ring of stacks over $\mathbb{C}$ is non-trivial and…

Relations among tautological classes on the moduli space of stable curves are obtained via the study of Witten's r-spin theory for higher r. In order to calculate the quantum product, a new formula relating the r-spin correlators in genus 0…

We prove a new convergence result for the slice spectral sequence, following work by Levine and Voevodsky. This verifies a derived variant of Voevodsky's conjecture on convergence of the slice spectral sequence. This is, in turn, a…

We construct closed symplectic manifolds for which spherical classes generate arbitrarily large subspaces in 2-homology, such that the first Chern class and cohomology class of the symplectic form both vanish on all spherical classes. We…