# Models and Fields: A delicate Passage to Characteristic p

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Jacob Tsimerman, Princeton University
Fine Hall 314

If a polynomial map from $C^n$ to itself is injective, then it is also surjective. The first proof of this elegant result actually used a passage to characteristic p. I'll introduce the relevant notions from model theory and explain the proof, which will naturally yield the following much stronger result: Every statement in the first order logic of rings is true in the algebraic closure of $F_p$ for almost all p iff it is true in C.