Opers of higher types, Quot-schemes and Frobenius instability loci

In this paper we continue our study of the Frobenius instability locus in the coarse moduli space of semi-stable vector bundles of rank r and degree 0 over a smooth projective curve defined over an algebraically closed field of characteristic p > 0. In a previous paper we identified the "maximal" Frobenius instability strata with opers (more precisely as opers of type 1 in the terminology of the present paper) and related them to certain Quot-schemes of Frobenius direct images of line bundles. The main aim of this paper is to describe for any integer q >= 1 a conjectural generalization of this correspondence between opers of type q and Quot-schemes of Frobenius direct images of vector bundles of rank q. We also give a conjectural formula for the dimension of the Frobenius instability locus.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu