Subject: BP_*BP comodules From: Mark Hovey Date: 23 Jan 1999 03:00:27 -0500 --------- I have been stumped by some basic questions about comodules over a Hopf algebroid (A, Gamma) for some time now. You can take A=BP_* and Gamma = BP_*BP if it helps. 1. A comodule I is relatively injective if for all A-split monomorphisms M --> N and maps M --> I, there is an extension N --> I. Do you have to use ALL A-split monomorphisms, or is there some subset you can get away with? Obvious candidates would be the subset where N is finitely generated over A, or the subset where N has cardinality not bigger than Gamma, or something like that. 2. If I is relatively injective, then Ext (M,I) =0 for all comodules M projective over A. Is the converse true? What I would like is: Ext^1(A,I) =0 implies I is relatively injective (at least for A=BP). Mark Hovey mhovey@wesleyan.edu