How is your representation theory stuff relevant to my work on Diophantine equations? :-P
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Replying to @peroxycarbonate
Well, in both subjects one often works with a system consisting of a ring of integers and its residue fields...
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Replying to @St_Rev
--where we think of the field of fractions as the residue 0 field, of course--and solving at the residue fields gives us local data
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Replying to @St_Rev
That said, I don't know much about group actions on diophantine systems. Although it would be interesting to lift my constructions
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Replying to @St_Rev
...from the kG category to the ZG category, where there are a lot of unsolved problems that might be addressed.
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Replying to @St_Rev
nb: this was off-the-cuff bullshitting. I know there are applications to number theory but I have no damn clue what they are.
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Replying to @St_Rev
Apparently it runs deep in the Langlands program though. http://www.math.harvard.edu/~chaoli/doc/EilenbergLectures.html …
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Replying to @St_Rev
Heh, "Langlands program" is always the answer. :-) But messy Diophantine eqs -> anabelian stuff -> current rep. theory fails?
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Replying to @peroxycarbonate
Oh no. Representation theory doesn't care much about commutative vs. non.
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Replying to @St_Rev
er, "anabelian" was probably the wrong term....not my specialty but also, stupid 140 character limit... http://people.maths.ox.ac.uk/kimm/papers/cambridgews.pdf … ?
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Oh. Motivic stuff is super hard, way over my head.
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.