Date
Tue, 24 Oct 2017
Time
15:45 - 16:45
Location
L4
Speaker
Udi Hrushovski
Organisation
Oxford

Hilbert's Nullstellensatz asserts the existence of a complex point satisfying lying on a given variety, provided there is no (ideal-theoretic) proof to the contrary.
I will describe an analogue for curves (of unbounded degree), with respect to conditions specifying that they lie on a given smooth variety, and have homology class
near a specified ray.   In particular, an analogue of the Lefschetz principle (relating large positive characteristic to characteristic zero) becomes available for such questions.
The proof is very close to a theorem of  Boucksom-Demailly-Pau-Peternell on moveable curves, but requires a certain sharpening.   This is part of a joint project with Itai Ben Yaacov, investigating the logic of the product formula; the algebro-geometric statement is needed for proving the existential closure of $\Cc(t)^{alg}$ in this language. 

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