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Bogomolev-Tian-Todorov theorem that the Kodaira-Spencer map of a local universal deformation of a Calabi-Yau manifold is an isomorphism. (
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https://math.stackexchange.com/questions/102252/english-translation-or-summary-of-relevements-modulo-p2-et-decomposition-du
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This page should include a discussion of (pre-)deformation functors with examples. A good resource for this material is
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I think this page should include a survey of some of the main theorems in deformation theory. This should include
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and let one of the coefficients be an infinite series. Each truncation gives a deformation of the curve over
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implies there exists a complete family of deformations where the kodaira-spencer map is an isomorphism
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Serre-Tate theorem (already there but should be developed further and moved to the theorems section)
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Discuss differential graded lie algebras and their use in deformation theory. Look at page 17 of
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http://web.archive.org/web/20151010220650/https://math.berkeley.edu/~achinger/notes/char-p-5.pdf
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This page should include the basic definitions from
Kodaira-Spencer theory, including the
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In addition, this should include examples both from geometry and arithmetic:
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discuss how deformation theory is the local study of
Hilbert schemes
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take examples of miniversal deformations from the milnor number page
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https://www.math.ucdavis.edu/~osserman/classes/256A/notes/deform.pdf
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Grothendieck's theorem on deformations of abelian varieties
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definition of deformations in the complex-analytic settings
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http://www.claymath.org/library/monographs/cmim01c.pdf
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This page should also discuss some of the material in
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Schlessinger's theorem (give non pro-representable)
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