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Meta
Tag Archives: K-theory
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 \(\mathrm{SL}(\mathbf{F}_p)\) 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
Posted in Mathematics, Uncategorized
Tagged completed cohomology, completed K-theory, Eric Friedlander, Evens, K-theory, stable cohomology
4 Comments
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
Posted in Mathematics
Tagged Borel, completed cohomology, K-theory, Milnor, Moore, Neisendorfer, Paul Goerss, Quillen, Soule
2 Comments
K_2(O_F) for number fields F
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
Posted in Mathematics
Tagged Alexander Rahm, Aurel Page, Banaszak, Belabas, Bloch, Borel, Brownkin, Chern class map, Euler System, Gangl, Higher Regulators, Hutchinson, K-theory, magma, pari, Popescu, Soule, Stark, Tricky Computation, Zagier
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Virtual Congruence Betti Numbers
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
Catalan’s Constant and periods
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
Posted in Mathematics
Tagged Apéry, Beukers, Gauss-Manin connection, Hypergeometric Functions, K-theory, Leopoldt Conjecture, Periods, Picard-Fuchs
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