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Compacto
  • Member for 3 years, 2 months
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What is sheaf cohomology intuitively?
I loved this answer. Seriously, I think this answer somehow made me see the light at the end of the sheaf cohomology tunnel.
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What are some concrete applications of Grothendieck's six operations?
Grothendieck was interested in a "complete" and general theory of cohomology, taking account of all the usual phenomena in the most general setting possible (the natural context where the notions have essential meaning, leaving concrete issues aside for later). Thus, his discovery of étale cohomology led him immediately to unveil a general formalism of derived categories. Meanwhile, most other mathematicians were primarily interested in the Weil Conject.(the applications of étale cohomology), and so, they gave less importance to the general "philosophy" (yoga) that inspired the development.
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On a series of lectures of Deligne on crystalline cohomology in characteristic $0$
@Emily Can you share it here? It would be useful to have it available for future searchers.
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What are dessins d'enfants?
True. I corrected the mistake about embedding curves in the plane and remarked that a dessin specifies the branched cover.
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What are dessins d'enfants?
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What are dessins d'enfants?
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What are dessins d'enfants?
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Did Grothendieck have a plan for proving Riemann Existence algebraically?
I think it's not correct to say that Grothendieck's vision "did not come to fruition", given that Deligne's proof is essentially based in étale cohomology and other ideas exposed by Groth in SGA 4 and 5. One thing is the main strategy to prove them (étale cohomology, envisioned by Groth) and another thing is the specific argument of proof (which Grothendieck expected to be motive theory/standard conjectures), which in the end was a great idea of Deligne which did not use standard conjectures.