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Number Theory Seminar

Title: Uniform irreducibility of Galois action on the $\ell$-primary part of Abelian $3$-folds of Picard type
Speaker: Mladen Dimitrov (University of Lille, France)
Date: 10 January 2023
Time: 10.30 AM
Venue: LH-1

Half a century ago Manin proved a uniform version of Serreā€™s celebrated result on the openness of the Galois image in the automorphisms of the $\ell$-adic Tate module of any non-CM elliptic curve over a given number field. In a collaboration with D. Ramakrishnan we provide first evidence in higher dimension. Namely, we establish a uniform irreducibility of Galois acting on the $\ell$-primary part of principally polarized Abelian $3$-folds of Picard type without CM factors, under some technical condition which is void in the semi-stable case. A key part of the argument is representation theoretic and relies on known cases of the Gan-Gross-Prasad Conjectures.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 21 Sep 2023