Answer by Piotr Achinger for What is the cotangent complex good for?
Here is an example mentioned in passing by user ali's answer, but I think it is cute (and powerful) enough to be worth fleshing out the details.Lifting from characteristic $p$ to characteristic zeroIn...
View ArticleAnswer by user1092847 for What is the cotangent complex good for?
Let me try to answer the questions in your edit. For the relationship to deformation theory, it is geometrically simpler to think about the tangent complex.Let $X$ be a smooth algebraic variety. Then...
View ArticleAnswer by ali for What is the cotangent complex good for?
If you want to see the relation between differential forms and deformation theory you can look at the part B of Illusie article in FGA explained which shows that why the obstruction to the problem of...
View ArticleAnswer by Pedro for What is the cotangent complex good for?
This is not down a stacky and geometric alley many people like, but I think it maybe useful to show how the (algebraic) cotangent complex can be used to organize and solve a very natural question of...
View ArticleAnswer by Harry Gindi for What is the cotangent complex good for?
One major application is in Artin's representablity theorem. Existence of a cotangent complex (what Artin calls existence of an obstruction theory) allows you to linearize the question of the existence...
View ArticleWhat is the cotangent complex good for?
The cotangent complex seems to be a pretty fundamental object in algebraic geometry, but if it's treated in Hartshorne then I missed it. It seems to be even more important in derived algebraic...
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