Thesis (Ph. D.)--University of Rochester. Dept. of Mathematics, 2013.
In this thesis we obtain a near-complete description of the E2 term of the Adams-Novikov spectral sequence converging to the homotopy groups of a spectrum Q(2). We do so by computing a double complex spectral sequence built from elliptic curve Hopf algebroids. The spectrum Q(2) was originally constructed by Behrens using degree 2 isogenies of elliptic curves, in order to better understand the K(2)-local sphere at the prime 3. Possible applications of our computation include studying how Q(2) detects elements of the beta family in the 3-primary stable stems, and proving a 3-primary analog of a theorem of Behrens, which characterizes the 2-line of the p-local Adams-Novikov spectral sequence for the sphere when p ≥ 5 in terms of congruence classes of modular forms. We plan to pursue these applications
in future work.
