KUMMER CRITERION OVER GLOBAL FUNCTION-FIELDS

[摘要] Let k be a global function field over the field F(q) where q = p(m) and let infinity be a fixed prime of k which we assume to have degree 1. We let A be the ring of functions holomorphic outside of infinity and we let p be a prime of A. Hayes has associated to {A, p} a finite abelian extension k(p) of k which is analogous to the classical cyclotomic extension Q(zeta(p)), where zeta(p) is a primitive pth root of unity. In this paper we define a certain set {B(i)} of A-fractional ideals of k (i.e., a set of finite divisors), and we establish an analog of Kummer's Theorem for {K(p), B(j)}. (C) 1994 Academic Press, Inc.

[发布日期] 1994-12-01