The Brauer group of cubic surfaces
1993 ◽
Vol 113
(3)
◽
pp. 449-460
◽
Keyword(s):
1. Let V be a non-singular rational surface defined over an algebraic number field k. There is a standard conjecture that the only obstructions to the Hasse principle and to weak approximation on V are the Brauer–Manin obstructions. A prerequisite for calculating these is a knowledge of the Brauer group of V; indeed there is one such obstruction, which may however be trivial, corresponding to each element of Br V/Br k. Because k is an algebraic number field, the natural injectionis an isomorphism; so the first step in calculating the Brauer–Manin obstruction is to calculate the finite group H1 (k), Pic .
Keyword(s):
1986 ◽
Vol 100
(2)
◽
pp. 237-248
◽
1981 ◽
Vol 89
(1)
◽
pp. 1-5
◽
Keyword(s):
1967 ◽
Vol 63
(3)
◽
pp. 693-702
◽
Keyword(s):
1981 ◽
Vol 33
(5)
◽
pp. 1074-1084
◽
1963 ◽
Vol 3
(4)
◽
pp. 408-434
◽
1976 ◽
Vol 15
(1)
◽
pp. 33-57
◽
1966 ◽
Vol 6
(4)
◽
pp. 399-401