Author Archives: Persiflage

The nearly ordinary deformation ring is (usually) torsion over weight space

Posted on September 19, 2014 by Persiflage

Let \(F/{\mathbf{Q}}\) be an arbitrary number field. Let \(p\) be a prime which splits completely in \(F\), and consider an absolutely irreducible representation: \(\rho: G_{F} \rightarrow {\mathrm{GL}}_2({\overline{\mathbf{Q}}}_p)\) which is unramified outside finitely many primes. If one assumes that \(\rho\) is … Continue reading →

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Tricky Fingers

Posted on September 18, 2014 by Persiflage

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 →

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The Artin conjecture is rubbish

Posted on September 10, 2014 by Persiflage

Let \(\rho: G_{\mathbf{Q}} \rightarrow \mathrm{GL}_N(\mathbf{C})\) be a continuous irreducible representation. Artin conjectured that the L-function \(L(\rho,s)\) is analytically continues to an entire function on \(\mathbf{C}\) (except for the trivial representation where the is a simple pole at one) and satisfies … 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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Intermezzo

Posted on September 3, 2014 by Persiflage

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 →

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100 Posts

Posted on August 19, 2014 by Persiflage

Meaningless numerical milestones are a good a reason as any for an indulgent post. Today, I will discuss some facts from this blog which you might not otherwise know about. It will be in the form of an (mercifully short) … Continue reading →

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The decline and fall of Publications Mathématiques de l’lHÉS

Posted on August 15, 2014 by Persiflage

I want to discuss the decline of a once great journal. How did IHES go from this: and this: to this: It is a sad state of affairs. To be clear, I am talking about the typesetting here. The old … Continue reading →

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Is Serre’s conjecture still open?

Posted on August 10, 2014 by Persiflage

The conjecture in this paper has indeed been proven. But that isn’t the entire story. Serre was fully aware of Katz modular forms of weight one. However, Serre was too timid was prudently conservative and made his conjecture only for … Continue reading →

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A flat white, please

Posted on August 10, 2014 by Persiflage

Thanks to the New York Times, I can now order a flat white at my local cafe instead of an 8 ounce latte. Culture is coming to America, my friends!

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Horizontal Vanishing Conjectures.

Posted on August 8, 2014 by Persiflage

Let \(F\) be a number field, and let \(\mathbf{G}\) be a reductive group over \(F\), and let \(\Gamma\) be a congruence subgroup of \(\mathbf{G}(\mathcal{O}_F)\). I can hear BC objecting that this doesn’t make sense without extra choices; if you have … Continue reading →

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