Related papers: Motivic Pontryagin classes and hyperbolic orientat…

We obtain a precise relation between the Chern-Schwartz-MacPherson class of a subvariety of projective space and the Euler characteristics of its general linear sections. In the case of a hypersurface, this leads to simple proofs of…

We prove that the (twisted orbifold) motives of the moduli spaces of $\mathrm{SL}_n$ and $\mathrm{PGL}_n$-Higgs bundles of coprime rank and degree on a smooth projective curve over an algebraically closed field in which the rank is…

We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanski\u{i}. The proof involves assigning a system of binary addresses to points in the Gromov boundary of…

Hierarchically hyperbolic spaces provide a common framework for studying mapping class groups of finite type surfaces, Teichm\"uller space, right-angled Artin groups, and many other cubical groups. Given such a space $\mathcal X$, we build…

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 study the category of $\mathbf{P}$-equivariant modules over the infinite variable polynomial ring, where $\mathbf{P}$ denotes the subgroup of the infinite general linear group $\mathbf{GL}(\mathbf{C}^\infty)$ consisting of elements…

We investigate representations of Coxeter groups into $\mathrm{GL}(n,\mathbb{R})$ as geometric reflection groups which are convex cocompact in the projective space $\mathbb{P}(\mathbb{R}^n)$. We characterize which Coxeter groups admit such…

Deligne and Goncharov constructed a neutral tannakian category of mixed Tate motives unramified over $\mathbb{Z}[\mu_N,1/N]$. Brown and Hain--Matsumoto computed the depth 2 quadratic relations of the motivic Galois group of this category…

This paper examines a number of related questions about Euler characteristics and characteristic classes with values in Witt cohomology. We establish a motivic version of the Becker-Gottllieb transfer, generalizing a construction of Hoyois.…

We provide a complete analysis of the motivic Adams spectral sequences converging to the bigraded coefficients of the 2-complete algebraic Johnson-Wilson spectra BPGL<n> over p-adic fields. These spectra interpolate between integral motivic…

We develop a theory of motivic spectra in a broad generality; in particular $\mathbb{A}^1$-homotopy invariance is not assumed. As an application, we prove that $K$-theory of schemes is a universal Zariski sheaf of spectra which is equipped…

For each prime $p$, we define a $t$-structure on the category $\widehat{S^{0,0}}/\tau\text{-}\mathbf{Mod}_{harm}^b$ of harmonic $\mathbb{C}$-motivic left module spectra over $\widehat{S^{0,0}}/\tau$, whose MGL-homology has bounded…

We compute the homotopy groups of the {\eta}-periodic motivic sphere spectrum over a finite-dimensional field k with characteristic not 2 and in which -1 a sum of four squares. We also study the general characteristic 0 case and show that…

We construct a comparison functor between ($\mathbf{A}^1$-local) tame motives and ($\overline{\square}$-local) log-\'etale motives over a field $k$ of positive characteristic. This generalizes Binda--Park--{\O}stv{\ae}r's comparison for the…

The theory of indices of Morse--Bott vector fields on a manifold is constructed and the famous localization problem for the transfer map is solved on its base in the present paper. As a consequence, we obtained addition theorems for the…

Call a normal complex projective variety $X$ Koll\'ar-hyperbolic if any nonconstant map from a smooth projective curve to $X$ induces a nontrivial homomorphism of \'etale fundamental groups. Examples include (a) smooth varieties with finite…

Let $M$ be a hyperkahler manifold, $\Gamma$ its mapping class group, and $Teich$ the Teichmuller space of complex structures of hyperkahler type. After we glue together birationally equivalent points, we obtain the so-called birational…

Let $R$ be a unital commutative ring with unit and $\mathscr{G}$ an ample groupoid. Using the topology of the groupoid $\mathscr{G}$, Steinberg defined an etale groupoid algebra $R\mathscr{G}$. These etale groupoid algebras generalize…

This article presents two key computations in MW-motivic cohomology. Firstly, we compute the MW-motivic cohomology of the symplectic groups $Sp_{2n}$ for any $n\in\mathbb{N}$ using the $Sp$-orientation and the associated Borel classes.…

Two semisimple algebraic groups of the same type are said to be motivic equivalent if the motives of the associated projective homogeneous varieties of the same type are isomorphic. We give general criteria of motivic equivalence in terms…