Geometric main conjectures in function fields

Abstract

Abstract We prove an equivariant main conjecture in Iwasawa theory along any rank-one, sign-normalized Drinfeld modular, split-at-∞ Iwasawa tower of a general function field of characteristic 𝑝, for the Iwasawa modules recently considered by Greither and Popescu in their proof of the classical equivariant main conjecture along the (arithmetic) cyclotomic Iwasawa tower. As a consequence, we prove an equivariant main conjecture for a projective limit of certain Ritter–Weiss type modules, along the same Drinfeld modular Iwasawa towers. This generalizes the results of Anglès, Bandini, Bars, Coscelli and Longhi for the split-at-∞ piece of the Iwasawa towers considered in their work, and refines the results by Greither and Popescu.

Locations

• arXiv (Cornell University) - View - PDF
• Journal für die reine und angewandte Mathematik (Crelles Journal) - View