Pullback and Strong Semistability on Algebraic Curves

Time: 10:30–11:30, 10 September, 2026

Venue: Room 612, Building A6

Online Zoom link:  https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

Abstract: This talk introduces the first phenomenon specific to positive characteristic: semistability need not be preserved by Frobenius pullback. We begin with the absolute and relative Frobenius morphisms and describe their effect on rank, degree, and slope. The canonical connection on a Frobenius pullback and its relation with the Harder–Narasimhan filtration will then be explained. Classical examples and existence results of Tango and Gieseker illustrate how Frobenius can destabilize a semistable bundle. This motivates the notion of strong semistability, requiring all iterated Frobenius pullbacks to remain semistable. We conclude with basic examples and structural properties of strongly semistable bundles, including their behavior under duals, twists, and tensor products.