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date: 2021-04-26
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Tags: #projects/review


- "Etale [groups schemes](groups%20schemes) are entirely determined by their geometric points."
- The basic idea for [deformation theory](deformation%20theory.md) is to understand when an object $X/S$ for $S$ a [scheme](scheme.md) lifts to an infinitesimal neighborhood of $S$.
  - Example: When does an [elliptic curve](elliptic%20curve.md) $E/\ZZ_p$ lift to an elliptic scheme $\mathcal E / \ZZ_p$?
- "Deformation theory for ‘blah’s is the study of smoothness for the [moduli space](moduli%20space.md) of ‘blah’s."
- "The deformation theory of an abelian scheme coincides with the deformation theory of its $p$-divisible group."
- $p\dash$divisible groups are systems (of finite, flat [group schemes](group%20scheme.md)) in which each piece is the torsion of the following piece.