Hecke modifications of vector bundles on the projective line over a finite field

Leonardo Soares Moço (ICMC, University of São Paulo)

Tuesday 11th February 15:00-16:00 Maths 311B

Abstract

A Hecke modification is a transformation of a vector bundle over a smooth curve that replaces its fibers at specified points, altering its structure while preserving its rank. Over the complex numbers, it is a fundamental tool for studying rank-2 parabolic bundles and is also known as an elementary transformation. Over a finite field, Hecke modifications play a key role in understanding the action of Hecke operators on spaces of automorphic forms. In this talk, I will present a classification of Hecke modifications of vector bundles over the projective line over a finite field, using the Hall algebra of coherent sheaves.

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