Bertini theorems in arithmetic geometry | Vidéo | Carmin.tv

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Bertini theorems in arithmetic geometry

By François Charles

Appears in collections : Rational points and algebraic geometry / Points rationnels et géométrie algébrique, Rational points and algebraic geometry / Points rationnels et géométrie algébrique

The classical Bertini irreducibility theorem states that if $X$ is an irreducible projective variety of dimension at least 2 over an infinite field, then $X$ has an irreducible hyperplane section. The proof does not apply in arithmetic situations, where one wants to work over the integers or a finite fields. I will discuss how to amend the theorem in these cases (joint with Bjorn Poonen over finite fields).

Information about the video

Date of recording 29/09/2016
Date of publication 02/02/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19056703
Cite this video CHARLES, François (29/09/2016). Bertini theorems in arithmetic geometry. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19056703
URL https://dx.doi.org/10.24350/CIRM.V.19056703

Domain(s)

Bibliography

Charles, F., & Poonen, B. (2016). Bertini irreducibility theorems over finite fields. Journal of the American Mathematical Society, 29(1), 81-94 - http://dx.doi.org/10.1090/S0894-0347-2014-00820-1

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