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Aug 17, 2010 at 8:45 vote accept Cosmonut
Aug 17, 2010 at 8:50
Aug 16, 2010 at 17:42 comment added Pete L. Clark I agree with all of this. I think McLarty's point of view makes some sense when FLT is read as a synecdoche for "modern arithmetic geometry using Grothendieck cohomologies". I am familiar with the foundations of etale cohomology and know that universes are absolutely not required there. However, for some other sites, things are less obviously benign. For an example -- which must be close to the simplest possible example -- of set-theoretic difficulties related to nilpotent thickenings, see Section 6 of math.uga.edu/~pete/apoints11.pdf.
Aug 16, 2010 at 16:44 comment added BCnrd Dear David: No problem. Dear Noah: Nice summary. Galois repns in pf of FLT are weight 2, built via Tate mods of Jacobians (no etale cohom). The part which gets some worked up about universes is Grothendieck duality (eliminated in the subsequent generalizations and improvements of the method, FWIW), but nothing in pfs of Gr. duality leads to universes either. Someone who reads the first proofs of original refs, as you suggest (bad idea: there's been progress!), won't run into universes. Too dramatic to focus on FLT. Would be better if those who speculate on certain proofs read them first. :)
Aug 16, 2010 at 16:27 history edited BCnrd CC BY-SA 2.5
semi-simple |---> semi-stable
Aug 16, 2010 at 16:06 comment added David E Speyer Note to BCnrd: It occurs to me that my edits make it trivial for someone to deduce your identity. I assume you have no intention of being genuinely anonymous but, if this bothers you, let me know and I will remove them.
Aug 16, 2010 at 16:05 comment added David E Speyer Edited to explain BCnrd's qualifications to those who don't already know them.
Aug 16, 2010 at 16:05 history edited David E Speyer CC BY-SA 2.5
added 637 characters in body
Aug 16, 2010 at 15:24 history answered Noah Snyder CC BY-SA 2.5