Author Archives: Persiflage

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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Life on the modular curve

Posted on September 24, 2013 by Persiflage

Alice and Bob live on the modular curve \(X_0(1) = \mathbf{H}/\mathrm{PSL}_2(\mathbb{Z})\). What does the world look like to them, assuming that they view the world in hyperbolic perspective? To those who are not used to hyperbolic geometry, there may be … Continue reading →

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Parenthood

Posted on September 9, 2013 by Persiflage

Some questions, I guess, one can’t be prepared for:

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En Passant III

Posted on August 31, 2013 by Persiflage

Question: When you are sick in bed, can you do any mathematics? I just spent the past few weeks with a sinus infection and was completely unable to do anything productive, that is, apart from writing an NSF grant (which … Continue reading →

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The Fundamental Curve of p-adic Hodge Theory, Part II

Posted on August 12, 2013 by Persiflage

This is a second post from JW, following on from Part I. The Galois group of \(\mathbb{Q}_p\) as a geometric fundamental group. In this follow-up post, I’d like to relay something Peter Scholze told me last fall. It concerns the … Continue reading →

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The Fundamental Curve of p-adic Hodge Theory, or How to Un-tilt a Tilted Field

Posted on July 23, 2013 by Persiflage

As Quomodocumque once said concerning the most recent set of courses at Arizona Winter School, “Jared Weinstein [gives] a great lecture.” On that note, I am delighted to welcome our first guest post, by the man himself. Note that it … Continue reading →

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Gerookte paling op de Albert Cuypmarkt

Posted on July 22, 2013 by Persiflage

My mother grew up in, as she would affectionately say, the rat infested slums of Amsterdam (complete with tales of giant rats crawling inside the toilet bowl and sleeping two to a bed). I finally had the chance to visit … Continue reading →

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Effective Motives

Posted on July 3, 2013 by Persiflage

This is a brief follow up concerning a question asked by Felipe. Suppose we assume the standard conjectures. Let \(M\) be a pure motive, and consider the following problems: Problem A: (“effectivity”) Suppose that \(M\) has non-negative Hodge-Tate weights. Then … Continue reading →

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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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Scholze on Torsion, Part III

Posted on June 22, 2013 by Persiflage

This is a continuation of Part I and Part II. Before I continue along to section V.3, I want to discuss an approach to the problem of constructing Galois representations from the pre-Scholze days. Let’s continue with the same notation … Continue reading →

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