Modular Curves of Infinite Level

نویسنده

  • JARED WEINSTEIN
چکیده

The goal of this course is to investigate an object which might be called X(p∞), and which appears as the inverse limit of the classical modular curves X(p). Informally, X(p∞) ought to classify elliptic curves E together with a Zp-basis for the Tate module Tp(E). (A disclaimer is in order, lest I be accused of false advertising: We won’t be studying all of X(p∞), but rather a piece of it corresponding to those E with supersingular reduction.) A recurring theme is that moduli spaces at infinite level can actually be simpler than their finite counterparts, although one must be willing to work with rings which are non-Noetherian.

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تاریخ انتشار 2012