I think it might be useful if we could all brainstorm theorems/derivations that we should memorize. I'll start, but others should feel free to edit this post.
Theorey
1. CAPM and 2 fund separation (monetary and zero-beta)
2. APT
3. First and Second fundamental Theorems of Asset Pricing
3.1 Conditions for Complete Markets Equilibrium
4. First and Second Welfare Theorems - Complete Markets
5. Milgrom and Stokey No Trade Theorems
Continuous Time
1. Ito's Lemma
2. Martingale Representation Theorem
3. Girsanov's Theorem
4. Black-Scholes Formula
Corporate
1. Modigliani Miller
2.
Microstructure
1. Kyle Model
2. Revenue Equivalence Theorem
3. Direct revelation principle
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