Publications at the Riemann Center
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 étale cohomology is, in general, not injective on torsion zero-cycles over finitely generated fields. This answers a question of Scavia and Suzuki.
Details
- Organisation(s)
-
Institute of Algebraic Geometry
Riemann Center for Geometry and Physics
- Type
- Article
- Journal
- Forum of Mathematics, Sigma
- Volume
- 11
- Publication date
- 22.06.2023
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Computational Mathematics, Analysis, Theoretical Computer Science, Discrete Mathematics and Combinatorics, Geometry and Topology, Algebra and Number Theory, Statistics and Probability, Mathematical Physics
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.2210.03201 (Access:
Open
)
https://doi.org/10.1017/fms.2023.51 (Access: Open )
