相关论文: The Hurewicz map in motivic homotopy theory

We prove that singular cohomology of the underlying space of Berkovich's analytification of a scheme $X$ locally of finite type over a trivially-valued field $k$ of characteristic $0$ is isomorphic to cdh-cohomology with integer…

We formulate a new theorem giving several necessary and sufficient conditions in order that a surjection of the fundamental group $\pi_1(X)$ of a compact K\"ahler manifold onto the fundamental group $\Pi_g$ of a compact Riemann surface of…

Let $A(G)$ and $B(H)$ be the Fourier and Fourier-Stieltjes algebras of locally compact groups $G$ and $H$, respectively. Ilie and Spronk have shown that continuous piecewise affine maps $\alpha: Y \subseteq H\rightarrow G$ induce completely…

Answering a question of Ed Schaefer, we show that if J is the Jacobian of a curve C over a number field, if s is an automorphism of J coming from an automorphism of C, and if u lies in the subring Z[s] of End J and has connected kernel,…

This paper constructs an h-model structure for diagrams of streams, locally preordered spaces. Along the way, the paper extends some classical characterizations of Hurewicz fibrations and closed Hurewicz cofibrations. The usual…

Let $X$ be an analytic space over a non-Archimedean, complete field $k$ and let $(f_1,..., f_n)$ be a family of invertible functions on $X$. Let $\phi$ the morphism $X\to G_m^n$ induced by the $f_i$'s, and let $t$ be the map $X\to…

Let $(X,o)$ be a complex normal surface singularity. We fix one of its good resolutions $\widetilde{X}\to X$, an effective cycle $Z$ supported on the reduced exceptional curve, and any possible (first Chern) class $l'\in…

The main theorem of this paper is that, for a general pair $(A,X)$ of an (ample) Hypersurface $X$ in an Abelian Variety $A$, the canonical map $\Phi_X$ of $X$ is birational onto its image if the polarization given by $X$ is not principal…

In this paper, we study the Nisnevich sheafification $\mathcal{H}^1_{\acute{e}t}(G)$ of the presheaf associating to a smooth scheme the set of isomorphism classes of $G$-torsors, for a reductive group $G$. We show that if $G$-torsors on…

We give a new proof, using comparatively simple techniques, of the Sullivan conjecture: the space of pointed maps from the classifying space of the cyclic group of order $p$ to any finite-dimensional CW complex $K$ is contractible.

Given a finite and connected two-dimensional $CW$-complex $K$ with fundamental group $\Pi$ and second integer cohomology group $H^2(K;\mathbb{Z})$ finite of odd order, we prove that: (1) for each local integer coefficient system…

We study the structure of the rational motivic stable homotopy category over general base schemes. Our first class of results concerns the six operations: we prove absolute purity, stability of constructible objects, and…

We prove some Liouville type results for generalized holomorphic maps in three classes: maps from pseudo-Hermitian manifolds to almost Hermitian manifolds, maps from almost Hermitian manifolds to pseudo-Hermitian manifolds and maps from…

We describe algebraically defined cohomological and homological Albanese and Picard 1-motives (or mixed motives) of any algebraic variety in characteristic zero, generalizing the classical Albanese and Picard varieties. We compute Hodge,…

Let $f: X \to Y$ be a dominant morphism of smooth, proper and geometrically integral varieties over a number field $k$, with geometrically integral generic fibre. We give a necessary and sufficient geometric criterion for the induced map…

We consider a generalized Riemann-Hurwitz formula as it may be applied to rational maps between projective varieties having an indeterminacy set and fold-like singularities. The case of a holomorphic branched covering map is recalled. Then…

In this paper, we construct and study derived character maps of finite-dimensional representations of $\infty$-groups. As models for $\infty$-groups we take homotopy simplicial groups, i.e. homotopy simplicial algebras over the algebraic…

Many important theorems in differential topology relate properties of manifolds to properties of their underlying homotopy types -- defined e.g. using the total singular complex or the \v{C}ech nerve of a good open cover. Upon embedding the…

Let $X$ be a variety. In this survey, we study (decompositions of) the motivic class, in the Grothendieck ring of stacks, of the stack $\mathscr{C}oh^n(X)$ of $0$-dimensional coherent sheaves of length $n$ on $X$. To do so, we review the…

Let G be an algebraic group corresponding to a compact Lie group. We study the restiction map from the Chow ring CH(BG) to the Wely group invariants CH(BT)^W. For example, we note that if G is simply connect and H(G) has torsion, then the…