Tag Archives: Matthew Emerton

Scholze on Torsion, Part IV

Posted on June 29, 2013 by Persiflage

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

Posted on May 18, 2013 by Persiflage

(This post is the result of a conversation I had with Matt). Suppose that \(\overline{\rho}: G_{F} \rightarrow \mathrm{GL}_n(\mathbf{F})\) is a continuous mod-\(p\) absolutely irreducible Galois representation. For now, let’s assume that \(F/F^{+}\) is a CM field, and \(\overline{\rho}\) is essentially … Continue reading →

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Torsion in the cohomology of co-compact arithmetic lattices

Posted on February 6, 2013 by Persiflage

Various authors (including Bergeron and Venkatesh) have shown that the cohomology of certain arithmetic groups have a lot of torsion. For example, if \(\Gamma\) is a co-compact arithmetic lattice in \(\mathrm{SL}_2(\mathbf{C})\), and \(\mathcal{L}\) is an acyclic local system, then \(\log … Continue reading →

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