School of Mathematics Seminars and Lectures

# Geometric local systems on generic curves

## by Prof. Najmuddin Fakhruddin (TIFR, Mumbai)

Wednesday, January 25, 2023 from to (Asia/Kolkata)
at AG-77
 Description Abstract: The talk will be based on parts of the preprint entitled Geometric local systems on very general curves and isomonodromy'' by Aaron Landesman and Daniel Litt (arXiv:2022.00039). A complex local system $L$ on a smooth projective curve $X$ over $\mathbb{C}$ is said to be geometric'' if there exists a smooth projective morphism $f:X \to U$, with $U$ a nonempty Zariski open subset of $X$, and an integer $i$ such that $L|_U$ is a direct summand of $R^i f_* \mathbb{C}_X$. The main result that we will discuss says that if the rank of $L$ is small compared to the genus of $X$, then the monodromy representation associated to $L$ must have finite image; this leads to counterexamples to conjectures of Budur--Wang and Esnault--Kerz.The proof uses methods from the theory of variations of Hodge structure.  Material: