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

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Authors

  • Theodosis Alexandrou
  • Stefan Schreieder
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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 journalArticleResearchpeer 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.
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