My question concerns a statement made by Fong and James in "Geometry of the Simple groups..."(1998); the statement says that they offer a proof "independent of etale methods." Am I to presume that "etale methods" are not as desirable as other methods in writing proofs? (I'm new to etale and hence may be oversensitive to what seems to be a judgement statement.) If etale methods are not desirable, obviously I would like to know why not. What is the down-side of etale methods?
To use Etale methods in proofs or not
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etale-cohomology
1 Answers
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"Étale" refers to methods from algebraic geometry, e.g., Étale morphism of schemes, Étale fundamental group, or Étale cohomology, and other things, used in number theory, algebraic geometry and other fields. This need not be "bad", of course. It just may be more technical than, say, abstract algebra. For this reason it may be desirable to have a proof "independent of these methods".