## 92.2 Examples of deformation problems

List of things that should go here:

1. Deformations of schemes:

1. The Rim-Schlessinger condition.

2. Computing the tangent space.

3. Computing the infinitesimal deformations.

4. The deformation category of an affine hypersurface.

2. Deformations of sheaves (for example fix $X/S$, a finite type point $s$ of $S$, and a quasi-coherent sheaf $\mathcal{F}_ s$ over $X_ s$).

3. Deformations of algebraic spaces (very similar to deformations of schemes; maybe even easier?).

4. Deformations of maps (eg morphisms between schemes; you can fix both or one of the target and/or source).

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