Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 00, Number 0, Pages 000000
S 0002-9947(XX)0000-0
CYCLES ON CURVES OVER GLOBAL FIELDS OF POSITIVE
CHARACTERISTIC
REZA AKHTAR
Abstract. Let k be a global field of positive characteristic and : X - Spec k
a smooth projective curve. We study the zero-dimensional cycle group V (X) =
Ker ( : SK1(X) K1(k)) and the one-dimensional cycle group W(X) = Coker (
:
K2(k) H0
Zar(X, K2)), 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.
1. Introduction
Let k be a global field of positive characteristic; that is, a field which is finitely
generated and of transcendence degree one over a finite field. Let : X - Spec k
be a smooth projective curve over k; consider the cycle groups

  

Source: Akhtar, Reza - Department of Mathematics and Statistics, Miami University (Ohio)

 

Collections: Mathematics