The Relative Brauer Group and Generalized Cross Products for a Cyclic Covering of Affine Space

  • TIMOTHY J. FORD, DRAKE M. HARMON
  • Published 2013

Abstract

We study algebras and divisors on a normal affine hypersurface defined by an equation of the form zn = f (x1, . . . ,xm). The coordinate ring is T = k[x1, . . . ,xm,z]/(z− f ), and if R = k[x1, . . . ,xm][ f−1] and S = R[z]/(zn − f ), then S is a cyclic Galois extension of R. If the Galois group is G, we show that the natural map H1(G,Cl(T ))→ H1(G,Pic(S… (More)

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