Algebra & Number Theory

Third Galois cohomology group of function fields of curves over number fields

Venapally Suresh

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Abstract

Let K be a number field or a p-adic field and F the function field of a curve over K. Let be a prime. Suppose that K contains a primitive -th root of unity. If =2 and K is a number field, then assume that K is totally imaginary. In this article we show that every element in H3(F,μ3) 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.

Article information

Source
Algebra Number Theory, Volume 14, Number 3 (2020), 701-729.

Dates
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
https://projecteuclid.org/euclid.ant/1593655269

Digital Object Identifier
doi:10.2140/ant.2020.14.701

Mathematical Reviews number (MathSciNet)
MR4113778

Subjects
Primary: 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]

Keywords
Galois cohomology functions fields number fields symbols

Citation

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


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