A Note on Dormant Opers of Rank  in Characteristic

Hoshi, Yuichiro

doi:10.1017/nmj.2018.4

Cited by 2 publications

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“…Corollary 4.2.4) and that N Op Zzz... n,X consists of exactly one element if n = 1. Also, by the duality of differential modules established in the first part of the present paper, we obtain the following assertions, generalizing [Wak1, Theorem A, (i) and (ii)], [Wak1,§ 4,Corollary 4.3.3], and [Hos1,Theorem A].…”

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Differential modules and dormant opers of higher level

Wakabayashi¹

2022

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In the first half of the present paper, we study higher-level generalizations of differential modules in positive characteristic. These objects may be regarded as ring-theoretic counterparts of vector bundles on a curve equipped with an action of the ring of (logarithmic) differential operators of finite level introduced by P. Berthelot (and C. Montagnon). The existence assertion for a cyclic vector of a differential module is generalized to higher level under mild conditions. In the second half, we introduce (dormant) opers of level N > 0 on a pointed smooth curve whose structure group is either GL n or PGL n . Some of the results on higher-level differential modules are applied to prove a duality theorem between dormant PGL n -opers of level N and dormant PGL p N −n -opers of level N . Finally, in the case where the underlying curve is a 3-pointed projective line, we establish a bijective correspondence between dormant PGL 2 -opers of level N and certain tamely ramified coverings.

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confidence: 69%

Differential modules and dormant opers of higher level

Wakabayashi¹

2022

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Frobenius-Affine Structures and Tango Curves

Hoshi

2022

Nagoya Math. J.

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In a previous paper, we discussed Frobenius-projective structures on projective smooth curves in positive characteristic and established a relationship between pseudo-coordinates and Frobenius-indigenous structures by means of Frobenius-projective structures. In the present paper, we discuss an “affine version” of this study of Frobenius-projective structures. More specifically, we discuss Frobenius-affine structures and establish a similar relationship between Tango functions and Frobenius-affine-indigenous structures by means of Frobenius-affine structures. Moreover, we also consider a relationship between these objects and Tango curves.

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A Note on Dormant Opers of Rank in Characteristic

Abstract: In this paper, we prove that the set of equivalence classes of dormant opers of rank $p-1$ over a projective smooth curve of genus ${\geqslant}2$ over an algebraically closed field of characteristic $p>0$ is of cardinality one.

Cited by 2 publications

References 6 publications

Differential modules and dormant opers of higher level

Differential modules and dormant opers of higher level

Frobenius-Affine Structures and Tango Curves

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