Cycles on curves over global fields of positive characteristic

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{c...

Full description

Saved in:
Bibliographic Details
Published in:Transactions of the American Mathematical Society 2005-07, Vol.357 (7), p.2557-2569
Main Author: Akhtar, Reza
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
College mathematics
Curves
Exact sciences and technology
Integers
Mathematical rings
Mathematical sequences
Mathematical theorems
Mathematics
Sciences and techniques of general use
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-05-03777-3