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.
"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