Two Cycle Class Maps on Torsion Cycles

Theodosis Alexandrou

doi:10.48550/arXiv.2401.11014

Details

Original language	English
Pages (from-to)	11625–11641
Number of pages	17
Journal	International Mathematics Research Notices
Volume	2024
Issue number	16
Early online date	19 Jun 2024
Publication status	Published - Aug 2024

Abstract

We compare two cycle class maps on torsion cycles and show that they agree up to a minus sign. The first one goes back to Bloch (1979), with recent generalizations to non-closed fields. The second is the \'etale motivic cycle class map \(\alpha^{i}_{X}\colon \text{CH}^{i}(X)_{\mathbb{Z}_{\ell}}\to H^{2i}_{L}(X,\mathbb{Z}_{\ell}(i))\) restricted to torsion cycles.

Keywords

math.AG, 14C15, 14C25 (Primary)

ASJC Scopus subject areas

Mathematics(all)
General Mathematics

Cite this

Two Cycle Class Maps on Torsion Cycles. / Alexandrou, Theodosis.
In: International Mathematics Research Notices, Vol. 2024, No. 16, 08.2024, p. 11625–11641.

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

Alexandrou, T 2024, 'Two Cycle Class Maps on Torsion Cycles', International Mathematics Research Notices, vol. 2024, no. 16, pp. 11625–11641. https://doi.org/10.48550/arXiv.2401.11014, https://doi.org/10.1093/imrn/rnae138

Alexandrou, T. (2024). Two Cycle Class Maps on Torsion Cycles. International Mathematics Research Notices, 2024(16), 11625–11641. https://doi.org/10.48550/arXiv.2401.11014, https://doi.org/10.1093/imrn/rnae138

Alexandrou T. Two Cycle Class Maps on Torsion Cycles. International Mathematics Research Notices. 2024 Aug;2024(16):11625–11641. Epub 2024 Jun 19. doi: 10.48550/arXiv.2401.11014, 10.1093/imrn/rnae138

Alexandrou, Theodosis. / Two Cycle Class Maps on Torsion Cycles. In: International Mathematics Research Notices. 2024 ; Vol. 2024, No. 16. pp. 11625–11641.

Download

@article{a3a94decb3c04581b111521b829437ae,

title = "Two Cycle Class Maps on Torsion Cycles",

abstract = " We compare two cycle class maps on torsion cycles and show that they agree up to a minus sign. The first one goes back to Bloch (1979), with recent generalizations to non-closed fields. The second is the \'etale motivic cycle class map \(\alpha^{i}_{X}\colon \text{CH}^{i}(X)_{\mathbb{Z}_{\ell}}\to H^{2i}_{L}(X,\mathbb{Z}_{\ell}(i))\) restricted to torsion cycles. ",

keywords = "math.AG, 14C15, 14C25 (Primary)",

author = "Theodosis Alexandrou",

year = "2024",

month = aug,

doi = "10.48550/arXiv.2401.11014",

language = "English",

volume = "2024",

pages = "11625–11641",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "16",

}

Download

TY - JOUR

T1 - Two Cycle Class Maps on Torsion Cycles

AU - Alexandrou, Theodosis

PY - 2024/8

Y1 - 2024/8

N2 - We compare two cycle class maps on torsion cycles and show that they agree up to a minus sign. The first one goes back to Bloch (1979), with recent generalizations to non-closed fields. The second is the \'etale motivic cycle class map \(\alpha^{i}_{X}\colon \text{CH}^{i}(X)_{\mathbb{Z}_{\ell}}\to H^{2i}_{L}(X,\mathbb{Z}_{\ell}(i))\) restricted to torsion cycles.

AB - We compare two cycle class maps on torsion cycles and show that they agree up to a minus sign. The first one goes back to Bloch (1979), with recent generalizations to non-closed fields. The second is the \'etale motivic cycle class map \(\alpha^{i}_{X}\colon \text{CH}^{i}(X)_{\mathbb{Z}_{\ell}}\to H^{2i}_{L}(X,\mathbb{Z}_{\ell}(i))\) restricted to torsion cycles.

KW - math.AG

KW - 14C15, 14C25 (Primary)

UR - http://www.scopus.com/inward/record.url?scp=85202069459&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2401.11014

DO - 10.48550/arXiv.2401.11014

M3 - Article

VL - 2024

SP - 11625

EP - 11641

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 16

ER -

Research@Leibniz University