Abstract
Let X be a smooth, projective curve of genus g ≥ 2 over an algebraically closed field of characteristic p > 0. I provide a conjectural formula for the degree of the scheme of dormant Projective General Linear PGL(r)-opers on X where r ≥ 2 (I assume that p is greater than an explicit constant depending on g, r). For r = 2, a dormant PGL(2)-oper is a dormant indigenous bundle on X in the sense of Shinichi Mochuzki (and his work provides a formula only for g = 2, r = 2, p ≥ 5, from a different point of view). In 2014, Yasuhiro Wakabayashi has shown that my conjectural formula holds for r = 2, g ≥ 2, and p > 2g - 2 and more recently he has proved the conjecture in all ranks for generic curves of genus at least two.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2599-2613 |
| Number of pages | 15 |
| Journal | International Mathematics Research Notices |
| Volume | 2017 |
| Issue number | 9 |
| DOIs | |
| State | Published - May 1 2017 |
ASJC Scopus subject areas
- General Mathematics
Fingerprint
Dive into the research topics of 'The degree of the dormant operatic locus'. Together they form a unique fingerprint.Cite this
- APA
- Standard
- Harvard
- Vancouver
- Author
- BIBTEX
- RIS