Title of Seminar: Algebraic Geometry Preprint Seminar 2025
Title of Talk: Essential dimension and Brosnan's conjecture
Speaker: Najmuddin Fakhruddin, TIFR, Mumbai
Date: March 17, 2025
Time: 16:00:00 Hours
Venue: AG-77
Abstract: The essential dimension of a generically finite map $f: X \to Y$ of varieties over a field $k$ is an integer between $0$ and $\dim(Y)$ which, in some sense, measures the complexity of $f$. A weak form of a conjecture of Brosnan states that if $n>1$ is any integer and $A$ is an abelian variety over a field of characteristic zero, then the essential dimension of the multiplication by $n$ map $[n]: A \to A$ is maximal, i.e., equals $\dim(A)$. After some work by the speaker with Saini and Farb--Kisin--Wolfson, the above statement was proven in full by Kollar and Zhuang (http://arxiv.org/abs/2402.15362v5). In this talk I will explain the main steps of their proof.
Title of Talk: Essential dimension and Brosnan's conjecture
Speaker: Najmuddin Fakhruddin, TIFR, Mumbai
Date: March 17, 2025
Time: 16:00:00 Hours
Venue: AG-77
Abstract: The essential dimension of a generically finite map $f: X \to Y$ of varieties over a field $k$ is an integer between $0$ and $\dim(Y)$ which, in some sense, measures the complexity of $f$. A weak form of a conjecture of Brosnan states that if $n>1$ is any integer and $A$ is an abelian variety over a field of characteristic zero, then the essential dimension of the multiplication by $n$ map $[n]: A \to A$ is maximal, i.e., equals $\dim(A)$. After some work by the speaker with Saini and Farb--Kisin--Wolfson, the above statement was proven in full by Kollar and Zhuang (http://arxiv.org/abs/2402.15362v5). In this talk I will explain the main steps of their proof.