The Relative Brauer Group of an Affine Double Plane |
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Authors: | Timothy J Ford |
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Institution: | 1. Department of Mathematics , Florida Atlantic University , Boca Raton , Florida , USA ford@fau.edu |
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Abstract: | We study algebra classes and divisor classes on a normal affine surface of the form z 2 = f(x, y). The affine coordinate ring is T = kx, y, z]/(z 2 ? f), and if R = kx, y]f ?1] and S = Rz]/(z 2 ? f), then S is a quadratic Galois extension of R. If the Galois group is G, we show that the natural map H1(G, Cl(T)) → H1(G, Pic(S)) factors through the relative Brauer group B(S/R) and that all of the maps are onto. Sufficient conditions are given for H1(G, Cl(T)) to be isomorphic to B(S/R). The groups and maps are computed for several examples. |
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Keywords: | Affine algebraic surface Brauer group Class group Picard group |
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