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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeMar 15th 2010
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   Author: zskoda
   Format: MarkdownI have created an entry [[ind-scheme]]. This is a slightly wider topic than [[formal scheme]], hence it deserves a separate entry, at least to record interesting references. Kapranov and Vasserot wrote a series of 4 articles in which they studied loop schemes, in a setup wider than those classifying loops in affine schemes (passage from affine to nonaffine situation is very nontrivial here, as the loops do not need to be localized so there is no descent property reducing it to loops in affine case), and an interesting result is the factorization monoid structure which is eventually responsible for factorization algebras in CFT. This should be compared to the approach via derived geometry a la Lurie and Ben-Zvi where topological loop spaces are used to obtain a similar structure.

   I have created an entry ind-scheme. This is a slightly wider topic than formal scheme, hence it deserves a separate entry, at least to record interesting references. Kapranov and Vasserot wrote a series of 4 articles in which they studied loop schemes, in a setup wider than those classifying loops in affine schemes (passage from affine to nonaffine situation is very nontrivial here, as the loops do not need to be localized so there is no descent property reducing it to loops in affine case), and an interesting result is the factorization monoid structure which is eventually responsible for factorization algebras in CFT. This should be compared to the approach via derived geometry a la Lurie and Ben-Zvi where topological loop spaces are used to obtain a similar structure.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 15th 2010
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   Author: Urs
   Format: MarkdownThanks, I need to eventually look into this.

   Thanks, I need to eventually look into this.

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeMar 15th 2010
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   Author: zskoda
   Format: MarkdownWell, this particular factorization monoid structure is responsible for a special chiral algebra (or if you like vertex operator algebra) of geometric origin and of a special importance (in certain equivalence of categories involving chiral algebras it corresponds to the identity endofunctor), so called chiral de Rham complex introduced by Gorbounov, Malikov and Schechtman.

   Well, this particular factorization monoid structure is responsible for a special chiral algebra (or if you like vertex operator algebra) of geometric origin and of a special importance (in certain equivalence of categories involving chiral algebras it corresponds to the identity endofunctor), so called chiral de Rham complex introduced by Gorbounov, Malikov and Schechtman.