The Brauer Group of a Rational Function Field over a Perfect Field

On the Hasse Principle for the Brauer group of a purely transcendental extension field in one variable over an arbitrary field

“…in [8]. But it is unknown fact whether ( 7) is exact or not in the case where k is not perfect and Theorem 3.5 has not been proved.…”

“…We call a statement of this form the Hasse principle. It is also known that the Hasse principle holds if K is a purely transcendental extension field in one variable over a perfect field k (see [8]). We show that it also holds without any assumption on k. The following is our main theorem.…”