Frobenius Direct Images, Canonical Filtrations, and Frobenius-Destabilized Bundles

Time: 14:30–16:30, 10 September, 2026

Venue: Room 612, Building A6

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

Abstract: This talk presents explicit constructions of stable vector bundles that become unstable after Frobenius pullback. We first study Frobenius direct images and recall the rank, degree, and stability properties of $(F_W)$. The main tool is the canonical filtration of $(F^F_W)$, whose graded pieces are $(W\otimes(\Omega_X^1)^{\otimes i})$. For a line bundle $(L)$, this filtration gives a concrete destabilizing subbundle of $(F^F_L)$, while $(F_L)$ itself is stable when the genus is at least two. We then discuss rank-two Frobenius-destabilized bundles, the Verschiebung map on moduli spaces, and the existence theorem of Lange–Pauly. In characteristic two, the particularly explicit classification and Frobenius stratification of Joshi–Ramanan–Xia–Yu will also be described.