Duality for Dormant Opers

J. Math. Sci. Univ. Tokyo
Vol. 24 (2017), No. 3, Page 271-320.

Wakabayashi, Yasuhiro
Duality for Dormant Opers
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Abstract:
In the present paper, we prove that on a fixed, pointed stable curve over a field of characteristic $p> 0$, there exists a $canonical$ duality between dormant $\mathfrak{sl}_\textrm{n}$-opers ($1 < n < p-1$) and dormant $\mathfrak{sl}_{(p-n)}$-opers, and that there exists a unique (up to isomorphism) dormant $\mathfrak{sl}_{(p-1)}$-oper.

Keywords: $p$-adic Teichm├╝ller theory, pointed stable curves, logarithmic connections, opers, dormant opers, $p$-curvature

Mathematics Subject Classification (2010): Primary 14H10, Secondly 14H60
Mathematical Reviews Number: MR3700485

Received: 2015-07-03