Vol. 14, No. 3, 2020

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

Venapally Suresh

Vol. 14 (2020), No. 3, 701–729

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.

Galois cohomology, functions fields, number fields, symbols
Mathematical Subject Classification 2010
Primary: 11R58
Received: 8 December 2018
Revised: 6 October 2019
Accepted: 22 November 2019
Published: 1 June 2020
Venapally Suresh
Department of Mathematics
Emory University
Atlanta, GA
United States