Details
Original language | English |
---|---|
Article number | e53 |
Journal | Forum of Mathematics, Sigma |
Volume | 11 |
Publication status | Published - 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
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Analysis
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Mathematical Physics
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In: Forum of Mathematics, Sigma, Vol. 11, e53, 22.06.2023.
Research output: Contribution to journal › Article › Research › peer review
}
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 -