Let F be a global function field of characteristic p with ring of integers A and let Φ be a Hayes module on the Hilbert class field H_A of F. We prove an Iwasawa Main Conjecture for the (Z_p)^∞-extension mathcal{F}/F generated by the mathfrak{p}-power torsion of Φ (mathfrak{p} a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or mathfrak{p}-adic characters, interpolates the Goss Zeta-function or some mathfrak{p}-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture.
Stickelberger series and Main Conjecture for function fields
andrea bandini;
2021-01-01
Abstract
Let F be a global function field of characteristic p with ring of integers A and let Φ be a Hayes module on the Hilbert class field H_A of F. We prove an Iwasawa Main Conjecture for the (Z_p)^∞-extension mathcal{F}/F generated by the mathfrak{p}-power torsion of Φ (mathfrak{p} a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or mathfrak{p}-adic characters, interpolates the Goss Zeta-function or some mathfrak{p}-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.