LOCAL-GLOBAL PRINCIPLES FOR ZERO-CYCLES ON HOMOGENEOUS SPACES OVER ARITHMETIC FUNCTION FIELDS

被引：2

作者：

Colliot-Thelene, J-L ^{[1
]}

Harbater, D. ^{[2
]}

Hartmann, J. ^{[2
]}

Krashen, D. ^{[3
]}

Parimala, R. ^{[4
]}

Suresh, V ^{[4
]}

机构：

[1] Univ Paris Saclay, Univ Paris Sud, Lab Math Orsay, CNRS, F-91405 Orsay, France

[2] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

[3] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[4] Emory Univ, Dept Math & Comp Sci, Atlanta, GA 30322 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 372卷 / 08期

关键词：

Linear algebraic groups and torsors; zero-cycles; local-global principles; semiglobal fields; discrete valuation rings; LINEAR ALGEBRAIC-GROUPS; VARIETIES; INDEX;

D O I：

10.1090/tran/7911

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the existence of zero-cycles of degree one on varieties that are defined over a function field of a curve over a complete discretely valued field. We show that local-global principles hold for such zero-cycles provided that local-global principles hold for the existence of rational points over extensions of the function field. This assertion is analogous to a known result concerning varieties over number fields. Many of our results are shown to hold more generally in the henselian case.

引用

页码：5263 / 5286

页数：24

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