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2020 Third Galois cohomology group of function fields of curves over number fields
Venapally Suresh
Algebra Number Theory 14(3): 701-729 (2020). DOI: 10.2140/ant.2020.14.701

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.

Citation

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Venapally Suresh. "Third Galois cohomology group of function fields of curves over number fields." Algebra Number Theory 14 (3) 701 - 729, 2020. https://doi.org/10.2140/ant.2020.14.701

Information

Received: 8 December 2018; Revised: 6 October 2019; Accepted: 22 November 2019; Published: 2020
First available in Project Euclid: 2 July 2020

MathSciNet: MR4113778
Digital Object Identifier: 10.2140/ant.2020.14.701

Subjects:
Primary: 11R58

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 3 • 2020
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