Opers de type supérieur, schémas Quot et lieux d’instabilité de Frobenius

Translated title of the contribution: Opers of higher types, Quot-schemes and Frobenius instability loci

Kirti Joshi, Christian Pauly

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Translated title of the contributionOpers of higher types, Quot-schemes and Frobenius instability loci
Original languageFrench
Article number17
JournalEpijournal de Geometrie Algebrique
Volume4
DOIs
StatePublished - Dec 8 2020

Keywords

  • Frobenius map
  • Oper
  • Quot-scheme
  • Semi-stability
  • Vector bundles

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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