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# Séminaire Théorie des Nombres

Responsables : Eric Balandraud, Dimitrios Chatzakos, Andrea Fanelli.

• Le 2 octobre 2020 à 14:00
• Salle de Conférence (en visio)
Francesca Balestrieri (American University of Paris)
Strong approximation for homogeneous spaces of linear algebraic groups
Building on work by Yang Cao, we show that any homogeneousspace of the form $G/H$ with $G$ a connected linear algebraic group over a number field $k$ satisfies strong approximation off the infinite places with étale-Brauer obstruction, under some natural compactness assumptions when $k$ is totally real. We also prove more refined strong approximation results for homogeneous spaces of the form $G/H$ with $G$ semisimple simply connected and $H$ finite, using the theory of torsors and descent. (This latter result is somewhat related to the Inverse Galois Problem.)
• Le 9 octobre 2020 à 14:00
• Salle de Conférence (en visio)
Efthymios Sofos (Glasgow)
Schinzel Hypothesis with probability 1 and rational points
Joint work with Alexei Skorobogatov, preprint: https://arxiv.org/abs/2005.02998.Schinzel's Hypothesis states that every integer polynomial satisfying certain congruence conditions represents infinitely many primes. It is one of the main problems in analytic number theory but is completely open, except for polynomials of degree 1. We describe our recent proof of the Hypothesis for 100% of polynomials (ordered by size of coefficients). We use this to prove that, with positive probability, Brauer--Manin controls the Hasse principle for Châtelet surfaces.
• Le 16 octobre 2020 à 14:00
• Salle 2
Elena Berardini (LIX - École polytechnique)
Titre à préciser

• Le 20 novembre 2020 à 14:00
• Salle de Conférence (en visio)
Xenia Spilioti (Aahrus)
Titre à préciser

• Le 27 novembre 2020 à 14:00
• Salle de Conférence (en visio)
Gabriel Dill (Oxford)
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