Category Archives: Math

Stacks in one sentence

A stack is just some rule which specifies a category of “wumbles over ” for every object in some given site, with the property that both morphisms of wumbles and wumbles themselves can be specified locally on coverings in the site. Bonus: Drop … Continue reading

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Rumor of the day

Mochizuki’s papers on inter-universal Teichmuller theory have been accepted by a journal. I heard this from a typically trustworthy full professor here at Columbia, whose name unfortunately won’t fit in this margin. Of course, even if this is true, it … Continue reading

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Superfectoid spaces!?

Note (6/21): There is an issue with the proof of Lemma 1.7 below, but I’m pretty confident Kiran and I will find a fix.  In any case, you should never take blog math too seriously! In this post I want to announce some … Continue reading

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Observations from Indiana

Just back from the p-adic Langlands party. Some random moments: Language options on the German American Banking ATM: English, Spanish. “We’ve encoded Kevin Buzzard’s brain into a two-variable power series!” Heated discussion: do you write or ?  Clearly the latter … Continue reading

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A Fitting remark

In this post I want to talk about an innocent commutative algebra lemma. Let be a DVR with uniformizer , and let be a finite torsion -module, so for some uniquely determined sequence . I’ll somewhat abusively refer to the … Continue reading

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God’s greatest creation?

I’m in California for 11 days, for (mostly) math.  Here’s something fun I just learned from Dick Gross.  Let be a split simple algebraic group over , and let be (a -lattice in) an irreducible algebraic representation of .  It’s not … Continue reading

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Period morphisms in p-adic Hodge theory

In classical Hodge theory, variations of Hodge structure give rise to varying periods, and then to period morphisms.  In p-adic Hodge theory, there are plenty of periods but (until recently) not so many period morphisms.  It turns out these exist … Continue reading

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