Algebra & Number Theory
- Algebra Number Theory
- Volume 14, Number 3 (2020), 701-729.
Third Galois cohomology group of function fields of curves over number fields
Let be a number field or a -adic field and the function field of a curve over . Let be a prime. Suppose that contains a primitive -th root of unity. If and is a number field, then assume that is totally imaginary. In this article we show that every element in is a symbol. This leads to the finite generation of the Chow group of zero-cycles on a quadric fibration of a curve over a totally imaginary number field.
Algebra Number Theory, Volume 14, Number 3 (2020), 701-729.
Received: 8 December 2018
Revised: 6 October 2019
Accepted: 22 November 2019
First available in Project Euclid: 2 July 2020
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]
Suresh, Venapally. Third Galois cohomology group of function fields of curves over number fields. Algebra Number Theory 14 (2020), no. 3, 701--729. doi:10.2140/ant.2020.14.701. https://projecteuclid.org/euclid.ant/1593655269