Tag Archives: Emerton

A Preview of Barbados/Bellairs

This post is probably not so interesting unless you plan to travel to the Caribbean in a few weeks. The website for the conference is offline, so I thought I might update attendees on what might be happening, at least … 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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Scholze on Torsion, Part IV

This is a continuation of Part I, Part II, and Part III. I was planning to start talking about Chapter IV, instead, this will be a very soft introduction to a few lines on page 72. At this point, we … Continue reading

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Finiteness of the global deformation ring over local deformation rings

(This post is the result of a conversation I had with Matt). Suppose that is a continuous mod- absolutely irreducible Galois representation. For now, let’s assume that is a CM field, and is essentially self-dual and odd. Associated to this … Continue reading

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Torsion in the cohomology of co-compact arithmetic lattices

Various authors (including Bergeron and Venkatesh) have shown that the cohomology of certain arithmetic groups have a lot of torsion. For example, if is a co-compact arithmetic lattice in , and is an acyclic local system, then The proof relies … Continue reading

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