M. Abboud - A bound on the action of nilpotent groups on complex algebraic varieties | Vidéo

M. Abboud - A bound on the action of nilpotent groups on complex algebraic varieties

Appears in collection : Summer School 2025 - Cremona Group

We discuss the following result. If G is a finitely generated nilpotent group acting faithfully on a complex algebraic variety X\, then the dimension of X is larger than the virtual derived length of G\, i.e the minimum of the derived length of the finite index subgroup of G. The proof uses p-adic analysis and p-adic Lie groups method. We show that up to finite index there exists a prime p such that G acts analytically on a p-adic manifold related to X. The study of this action gives the desired bound.