The Stacks project

113.7 Deformation theory à la Schlessinger

We have a chapter on this material, see Formal Deformation Theory, Section 90.1. We have a chapter discussing examples of the general theory, see Deformation Problems, Section 93.1. We have a chapter, see Deformation Theory, Section 91.1 which discusses deformations of rings (and modules), deformations of ringed spaces (and sheaves of modules), deformations of ringed topoi (and sheaves of modules). In this chapter we use the naive cotangent complex to describe obstructions, first order deformations, and infinitesimal automorphisms. This material has found some applications to algebraicity of moduli stacks in later chapters. There is also a chapter discussing the full cotangent complex, see Cotangent, Section 92.1.

Comments (4)

Comment #196 by Emmanuel Kowalski on

Pedantically speaking, "a la Schlessinger" should be "`a la Schlessinger"...

Comment #197 by Emmanuel Kowalski on

(and a backslash got skipped in the comment... ("à la Schlessinger")

Comment #198 by on

I notice that there is a character encoding issue. I will look into this.

Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 02BF. Beware of the difference between the letter 'O' and the digit '0'.