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Status: planning

Problem: find a practical way to compute the Ext of the BP Hopf-algebroid.

Recall Miller's algebraic Novikov spectral sequence
^{odd} denotes the "oddified" associated graded of the Steenrod algebra.
One way to set up this spectral sequence is based on
the spectrum
_{p}
and there is a related differential on EBP with
∂(β_{i}) = v_{i}.

The cooperations EBP_{*}EBP form a differential Hopf algebroid
whose ∂-homology is the Hopf algebra dual to A^{odd}. Miller's
spectral sequence can then be realized by computing a lift K of
an A^{odd}-resolution into the world of EBP_{*}EBP-modules.

I vaguely think that the following might be true:

**Idea 1:**
Such a lift K can be computed recursively as K/I^n for n=1,2,...

Here K/I^{n}
should require computations in EBP_{*}EBP/I^{n+1}
and leave K/I^{n-1} alone.

**Idea 2:**
You only need K/I to draw a chart of the
algebraic Novikov spectral sequence (including extensions).

Combined these ideas might lead to a little miracle: a computation of the Ext of BP_{*}BP
which only requires working in EBP_{*}EBP/I^{2}.

Ext_{Aodd}(F_{p}) ⇒
Ext_{BP*BP}(BP_{*})

where AEBP = BP ⊗ E(β_{0}, β_{1},...)

Here EBP should be understood as a wedge of suspended copies of BP.
EBP is an associated graded of the Eilenberg-MacLane spectrum HFThe cooperations EBP

I vaguely think that the following might be true:

Here K/I

Combined these ideas might lead to a little miracle: a computation of the Ext of BP