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

H\'el\`ene Esnault; Olivier Wittenberg

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1305.1182 v4 pith:OMNXM3IN submitted 2013-05-06 math.AG math.NT

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

H\'el\`ene Esnault , Olivier Wittenberg This is my paper

classification math.AG math.NT

keywords localfieldsclasssurfacescyclestrictlyzero-cyclescharacteristic

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original 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.

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Obstruction sequences to homotopy equivalences
math.AT 2025-09 conditional novelty 6.0

Gauge-theoretic obstruction sequences characterize homotopy equivalences between algebras over properads and colored operads, with applications to minimal models over general fields and in etale cohomology.