点付き安定曲線上の休眠乍の数え上げ : 研究報告 (Algebraic Number Theory and Related Topics 2014)

Abstract

This article includes a partial explanation of the diversity of (dormant) opers (and their moduli) as well as a research announcement for some results of the paper titled "A theory of dormant opers on pointed stable curves--a proof of Joshi's conjecture--" (cf. [18]). First, we recall the notion of a projective structure (as well as an indigenous bundle) defined on a Riemann surface, which is equivalent to the notion of an sl2-oper. Next, we give the definition of a dormant g-oper (for each semisimple Lie algebra g), which is defined on an algebraic curve in positive characteristic. Finally, we propose some results, concerning an explicit computation of the number of dormant opers on a sufficiently general curve.