On Bloch's map for torsion cycles over non-closed fields

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Theodosis Alexandrou
  • Stefan Schreieder

Research Organisations

View graph of relations

Details

Original languageEnglish
Article numbere53
JournalForum of Mathematics, Sigma
Volume11
Publication statusPublished - 22 Jun 2023

Abstract

We generalize Bloch's map on torsion cycles from algebraically closed fields to arbitrary fields. While Bloch's map over algebraically closed fields is injective for zero-cycles and for cycles of codimension at most two, we show that the generalization to arbitrary fields is only injective for cycles of codimension at most two but, in general, not for zero-cycles. Our result implies that Jannsen's cycle class map in integral -adic continuous étale cohomology is, in general, not injective on torsion zero-cycles over finitely generated fields. This answers a question of Scavia and Suzuki.

Keywords

    math.NT, math.AG, 14C15, 14C25, 14C15 14C25 14D06

ASJC Scopus subject areas

Cite this

On Bloch's map for torsion cycles over non-closed fields. / Alexandrou, Theodosis; Schreieder, Stefan.
In: Forum of Mathematics, Sigma, Vol. 11, e53, 22.06.2023.

Research output: Contribution to journal › Article › Research › peer review

Alexandrou, T., & Schreieder, S. (2023). On Bloch's map for torsion cycles over non-closed fields. Forum of Mathematics, Sigma, 11, Article e53. https://doi.org/10.48550/arXiv.2210.03201, https://doi.org/10.1017/fms.2023.51
Alexandrou T, Schreieder S. On Bloch's map for torsion cycles over non-closed fields. Forum of Mathematics, Sigma. 2023 Jun 22;11:e53. doi: 10.48550/arXiv.2210.03201, 10.1017/fms.2023.51
Alexandrou, Theodosis ; Schreieder, Stefan. / On Bloch's map for torsion cycles over non-closed fields. In: Forum of Mathematics, Sigma. 2023 ; Vol. 11.
Download
@article{b9447e98da6b4954a7c21a4d56e64323,
title = "On Bloch's map for torsion cycles over non-closed fields",
abstract = "We generalize Bloch's map on torsion cycles from algebraically closed fields to arbitrary fields. While Bloch's map over algebraically closed fields is injective for zero-cycles and for cycles of codimension at most two, we show that the generalization to arbitrary fields is only injective for cycles of codimension at most two but, in general, not for zero-cycles. Our result implies that Jannsen's cycle class map in integral -adic continuous {\'e}tale cohomology is, in general, not injective on torsion zero-cycles over finitely generated fields. This answers a question of Scavia and Suzuki.",
keywords = "math.NT, math.AG, 14C15, 14C25, 14C15 14C25 14D06",
author = "Theodosis Alexandrou and Stefan Schreieder",
note = "Funding Information: We thank the referee for his or her useful comments. This project has received funding from the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme under grant agreement No 948066 (ERC-StG RationAlgic).",
year = "2023",
month = jun,
day = "22",
doi = "10.48550/arXiv.2210.03201",
language = "English",
volume = "11",

}

Download

TY - JOUR

T1 - On Bloch's map for torsion cycles over non-closed fields

AU - Alexandrou, Theodosis

AU - Schreieder, Stefan

N1 - Funding Information: We thank the referee for his or her useful comments. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 948066 (ERC-StG RationAlgic).

PY - 2023/6/22

Y1 - 2023/6/22

N2 - We generalize Bloch's map on torsion cycles from algebraically closed fields to arbitrary fields. While Bloch's map over algebraically closed fields is injective for zero-cycles and for cycles of codimension at most two, we show that the generalization to arbitrary fields is only injective for cycles of codimension at most two but, in general, not for zero-cycles. Our result implies that Jannsen's cycle class map in integral -adic continuous étale cohomology is, in general, not injective on torsion zero-cycles over finitely generated fields. This answers a question of Scavia and Suzuki.

AB - We generalize Bloch's map on torsion cycles from algebraically closed fields to arbitrary fields. While Bloch's map over algebraically closed fields is injective for zero-cycles and for cycles of codimension at most two, we show that the generalization to arbitrary fields is only injective for cycles of codimension at most two but, in general, not for zero-cycles. Our result implies that Jannsen's cycle class map in integral -adic continuous étale cohomology is, in general, not injective on torsion zero-cycles over finitely generated fields. This answers a question of Scavia and Suzuki.

KW - math.NT

KW - math.AG

KW - 14C15, 14C25

KW - 14C15 14C25 14D06

UR - http://www.scopus.com/inward/record.url?scp=85164349069&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2210.03201

DO - 10.48550/arXiv.2210.03201

M3 - Article

VL - 11

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - e53

ER -