Tag Archives: completed cohomology

The stable cohomology of SL(F_p)

Back by popular demand: an actual mathematics post! Today’s problem is the following: compute the cohomology of for a (mod-p) algebraic representation. Step 0 is to say what this problem actually is. It makes sense to talk about certain algebraic … Continue reading

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Ventotene, Part II

I promised to return to a more mathematical summary of the conference in Ventotene, and indeed I shall do so in the next two posts. One of the themes of the conference was bounding the order of the torsion subgroup … Continue reading

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In this post (which is a follow-up to the last post), I wanted to compute the group , where is the congruence subgroup of for large enough and is prime. In fact, to make my life easier, I will also … Continue reading

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Stable completed homology without Quillen-Lichtenbaum

Having just made (hopefully) the final revisions on my paper on stable completed cohomology groups, I wanted to record here a few remarks which didn’t otherwise make it into the paper. The first is that, in addition to the result … Continue reading

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Local representations occurring in cohomology

Michael Harris was in town for a few days, and we chatted about the relationship between my conjectures on completed cohomology groups with Emerton and the recent work of Scholze. The brief summary is that Scholze’s results are not naively … Continue reading

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Virtual Congruence Betti Numbers

Suppose that is a real semisimple group and that is a compact arithmetic locally symmetric space. Let us call a cohomology class tautological if it is invariant under the group . For example, if is a 3-manifold, then the tautological … Continue reading

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