Cycles on curves over global fields of positive characteristic
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Abstract:
Let $k$ be a global field of positive characteristic, and let $\sigma : X \longrightarrow \operatorname {Spec} k$ be a smooth projective curve. We study the zero-dimensional cycle group $V(X) =\operatorname {Ker}(\sigma _*: SK_1(X) \rightarrow K_1(k))$ and the one-dimensional cycle group $W(X) =\operatorname {coker}(\sigma ^*: K_2(k) \rightarrow H^0_{Zar}(X, \mathcal {K}_2))$, addressing the conjecture that $V(X)$ is torsion and $W(X)$ is finitely generated. The main idea is to use Abhyankar’s Theorem on resolution of singularities to relate the study of these cycle groups to that of the $K$-groups of a certain smooth projective surface over a finite field.References
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Additional Information
- Reza Akhtar
- Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
- Email: reza@calico.mth.muohio.edu
- Received by editor(s): January 20, 2003
- Published electronically: March 1, 2005
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 2557-2569
- MSC (2000): Primary 14C15, 14C25
- DOI: https://doi.org/10.1090/S0002-9947-05-03777-3
- MathSciNet review: 2139518