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Tag Archives: Emerton
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
Posted in Mathematics
Tagged completed cohomology, Emerton, Michael Harris, Scholze, torsion
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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 3manifold, then the tautological … Continue reading
Posted in Mathematics
Tagged Agol, Boston, completed cohomology, congruence subgroups, Dunfield, Ellenberg, Emerton, homology spheres, Ktheory
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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
Posted in Mathematics
Tagged Emerton, Fargues, Galois Representations, Geraghty, Langlands, Mantovan, Reduzzi, Scholze, torsion, Weinstein, Xiao
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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 selfdual and odd. Associated to this … Continue reading
Posted in Mathematics
Tagged BLGGT, Emerton, Galois Representations, Geraghty, Paskunas, Thorne
3 Comments
Torsion in the cohomology of cocompact 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 cocompact arithmetic lattice in , and is an acyclic local system, then The proof relies … Continue reading
Posted in Mathematics
Tagged Bergeron, Emerton, Iwasawa Theory, Ouroboros, Poincare Duality, torsion, Venkatesh
4 Comments