Publications of the Research Institute for Mathematical Sciences


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Volume 50, Issue 3, 2014, pp. 383–409
DOI: 10.4171/PRIMS/138

Published online: 2014-09-17

An Explicit Formula for the Generic Number of Dormant Indigenous Bundles

Yasuhiro Wakabayashi[1]

(1) Kyoto University, Japan

A dormant indigenous bundle is an integrable $\mathbb P^1$-bundle on a proper hyperbolic curve of positive characteristic satisfying certain conditions. Dormant indigenous bundles were introduced and studied in $p$-adic Teichmuller theory developed by S. Mochizuki. Kirti Joshi proposed a conjecture concerning an explicit formula for the degree over the moduli stack of curves of the moduli stack classifying dormant indigenous bundles. In this paper, we give a proof for this conjecture.

Keywords: $p$-adic Teichmuller theory, indigenous bundles, opers, $p$-curvature

Wakabayashi Yasuhiro: An Explicit Formula for the Generic Number of Dormant Indigenous Bundles. Publ. Res. Inst. Math. Sci. 50 (2014), 383-409. doi: 10.4171/PRIMS/138