Citation/Abstract

This work is a partially successful attempt to produce a homology theory that comes from elliptic curves endowed with a p ⁿ -level structure over a field of characteristic p . Following the idea of Michael J. Hopkins and his collaborators we know that the homology theory of our interest can be constructed as the connected cover of the pullback of the diagram consisting of K (1) and K (2)-local models for it. We produce a K (1)-local tmf with p ⁿ -level structures, as well as K (2)-local tmf with p ⁿ -level structures for cases p = 3 and n = 1, and p > 3 and arbitrary n .