On the cycle class map for zero-cycles over local fields

Hélène Esnault; Olivier Wittenberg

doi:10.24033/asens.2288

Home/Archive/arXiv

arXiv · 1305.1182

On the cycle class map for zero-cycles over local fields

Hélène Esnault·Olivier Wittenberg

View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the Chow group of zero-cycles of smooth projective varieties over local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus, over local fields of residue characteristic different from l. The same statement holds for semistable K3 surfaces defined over C((t)), but does not hold in general for surfaces over strictly local fields.

Explore related subjects

math.AG math.NT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Hélène Esnault, Olivier Wittenberg. 2015-12-19. On the cycle class map for zero-cycles over local fields. https://doi.org/10.24033/asens.2288

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

K-stable Fano 3-folds in the families 2.18 and 3.4

We prove that smooth Fano 3-folds in the families 2.18 and 3.4 are K-stable.

math.AG↗

arXiv2026

G3-Criteria and Applications

The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.

math.AG↗

arXiv2026

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG↗