Tag Archives: K-theory

The stable cohomology of SL(F_p)

Posted on June 19, 2019 by Persiflage

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

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Stable completed homology without Quillen-Lichtenbaum

Posted on January 21, 2015 by Persiflage

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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K_2(O_F) for number fields F

Posted on September 4, 2014 by Persiflage

Belabas and Gangl have a nice paper ( Generators and relations for \(K_2({\mathcal{O}}_F)\), which can be found here) where they compute \(K_2({\mathcal{O}}_E)\) for a large number of quadratic fields \(E\). There main result is a method for proving upper bounds … Continue reading →

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Virtual Congruence Betti Numbers

Posted on September 27, 2013 by Persiflage

Suppose that \(G\) is a real semisimple group and that \(X = \Gamma \backslash G/K\) is a compact arithmetic locally symmetric space. Let us call a cohomology class tautological if it is invariant under the group \(G\). For example, if … Continue reading →

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Catalan’s Constant and periods

Posted on May 4, 2013 by Persiflage

There is a 60th birthday conference in honour of Frits Beukers in Utrech in July; I’m hoping to swing by there on the way to Oberwolfach. Thinking about matters Beukers made me reconsider an question that I’ve had for while. … Continue reading →

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