Algebra & Number Theory

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

Venapally Suresh

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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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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

Galois cohomology functions fields number fields symbols


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.

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