Related papers: Remarks on cycle classes of sections of the arithm…

Let k be an algebraically closed field and X a smooth projective k-variety. A famous theorem of A. A. Roitman states that the canonical map from the degree zero part of the Chow group of zero cycles on X to the group of k-points of its…

We consider a product $X=E_1\times\cdots\times E_d$ of elliptic curves over a finite extension $K$ of $\mathbb{Q}_p$ with a combination of good or split multiplicative reduction. We assume that at most one of the elliptic curves has…

Let $f : X \to S$ be a smooth projective family defined over $\mathcal{O}_{K}[\mathcal{S}^{-1}]$, where $K \subset \mathbb{C}$ is a number field and $\mathcal{S}$ is a finite set of primes. For each prime $\mathfrak{p} \in…

We show that every cycle in the degree $d$ algebraic cobordism group $\Omega_d(X)$ of a smooth projective variety $X$ over a field of characteristic $0$ is smoothable when $2d<\dim(X)$, that is, it can be written as a linear combination of…

Let $K$ be the function field of a smooth projective geometrically integral curve over a finite extension of $\mathbb{Q}_p$. Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local-global and weak…

We define a category whose objects are finite etale coverings of an algebraic stack and prove that it is a Galois category and that it allows one to compute the fundamental group of the stack. We then prove a Van Kampen theorem for…

Using Galois-Stiefel-Whitney classes of theta characteristics we show that over a totally real base field the moduli stack of smooth genus $g$ curves and the moduli stack of principally polarized abelian varieties of dimension $g$ have…

We investigate a certain class of (geometric) finite (Galois) coverings of formal fibres of $p$-adic curves and the corresponding quotient of the (geometric) \'etale fundamental group. A key result in our investigation is that these…

For a quasi-projective smooth scheme X of pure dimension d over a field k and an effective Cartier divisor D on X whose support is a simple normal crossing divisor, we construct a cycle class map from the Chow group of zero-cycles with…

Let $K$ be the fraction field of a complete discrete valuation ring, with algebraically closed residue field of characteristic $p > 0$. This paper studies the index of a smooth, proper $K$-variety $X$ with logarithmic good reduction. We…

This paper is devoted to the explicit description of the Galois descent obstruction for hyperelliptic curves of arbitrary genus whose reduced automorphism group is cyclic of order coprime to the characteristic of their ground field. Along…

In this article we prove a semistable version of the variational Tate conjecture for divisors in crystalline cohomology, stating that a rational (logarithmic) line bundle on the special fibre of a semistable scheme over $k [\![ t ]\!]$…

In this paper we study the semi-stable reduction of $p$ and $p^2$-cyclic covers of curves in equal characteristic $p>0$. The main tool we use is the classical Artin-Schreier-Witt theory for $p^n$-cyclic covers in characteristic $p$.…

We study the moduli spaces which classify smooth surfaces along with a complex line bundle. There are homological stability and Madsen--Weiss type results for these spaces (mostly due to Cohen and Madsen), and we discuss the cohomological…

A conjecture of Colliot-Th\'{e}l\`{e}ne predicts that for a smooth projective variety $X$ over a finite extension $k$ of $\mathbb{Q}_p$ the kernel of the Albanese map $\text{CH}_0(X)^{\text{deg}=0}\to Alb_X(k)$ is the direct sum of a…

We study torsors under finite group schemes over the punctured spectrum of a singularity $x\in X$ in positive characteristic. We show that the Dieudonn\'e module of the (loc,loc)-part $\mathrm{Picloc}^{\mathrm{loc},\mathrm{loc}}_{X/k}$ of…

We establish a valuative version of Grothendieck's section conjecture for curves over p-adic local fields. The image of every section is contained in the decomposition subgroup of a valuation which prolongs the p-adic valuation to the…

For a smooth geometrically integral variety $X$ over a field $k$ of characteristic 0, we introduce and investigate the extended Picard complex $UPic(X)$. It is a certain complex of Galois modules of length 2, whose zeroth cohomology is…

We consider algebras over a field $k$ of characteristic zero. The article is concerned with the isomorphism of graded vectorspaces \[ H(\gl(A))\iso\wedge (HC(A)[-1]) \] between the Lie algebra homology of matrices and the free graded…

In this paper we extend the unramified class field theory for arithmetic surfaces of K. Kato and S. Saito to the relative case. Let X be a regular proper arithmetic surface and let Y be the support of divisor on X. Let CH_0(X,Y) denote the…