Seminar Event Detail

Student Algebraic Geometry

Date:  Friday, October 15, 2021
Location:  2866 East Hall (3:00 PM to 4:00 PM)

Title:  Logic and Algebraic Geometry in The Ax-Grothendieck Theorem

Abstract:   Let $k$ be an algebraically closed field and $V$ a variety over $k$. The Ax Grothendieck Theorem states that any algebraic endomorphism of $V$ injective on the $k$-points is bijective. Trivial if $k$ is replaced by a finite field, in the characteristic 0 case even when $k=C$ and $V$ is a complex vector space, the theorem is far from obvious. In this talk we will prove the theorem by showing a method of reducing the char 0 case to char p, and then time permitting discuss how this result can be interpreted as exhibiting the model independence of a certain logical class of algebraic statements, thus allowing a general technique of translating between different field-theoretic contexts.


Speaker:  Matthew Sawoski
Institution:  UM

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