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Monthly Archives: September 2014
Applying for an NSF grant
It’s not easy to write a good grant proposal. But it can be even harder to write one for the first time, especially if you’re not quite sure who will be reading your proposal. So today, I want to say … Continue reading
The nearly ordinary deformation ring is (usually) torsion over weight space
Let be an arbitrary number field. Let be a prime which splits completely in , and consider an absolutely irreducible representation: which is unramified outside finitely many primes. If one assumes that is geometric, then the Fontaine–Mazur conjecture predicts that … Continue reading
Tricky Fingers
How is one supposed to play this exactly? One can neither can play a 14th in the right hand (my hands are not that big) nor play legato parallel 10ths in the left; hence some sort of arpeggiation is required. … Continue reading
The Artin conjecture is rubbish
Let be a continuous irreducible representation. Artin conjectured that the Lfunction is analytically continues to an entire function on (except for the trivial representation where the is a simple pole at one) and satisfies a functional equation of a precise … Continue reading
Posted in Mathematics
Tagged Andrew Booker, Artin, Cebotarev Density Theorem, Class Number Problem, Goldfeld, GRH, Gross, Jo Dwyer, Langlands, Rubbish, Springer, Stark, Zagier
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K_2(O_F) for number fields F
Belabas and Gangl have a nice paper ( Generators and relations for , which can be found here) where they compute for a large number of quadratic fields . There main result is a method for proving upper bounds for … Continue reading
Posted in Mathematics
Tagged Alexander Rahm, Aurel Page, Banaszak, Belabas, Bloch, Borel, Brownkin, Chern class map, Euler System, Gangl, Higher Regulators, Hutchinson, Ktheory, magma, pari, Popescu, Soule, Stark, Tricky Computation, Zagier
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Intermezzo
Scholze is giving a course at Berkeley! Follow Jared Weinstein’s lecture notes from the course here. I believe that the lectures are also being recorded and will be available approximately one week after each lecture; I will add a link … Continue reading