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Duality for dormant opers of classical types B and C
Yasuhiro Wakabayashi
A -oper for a simple Lie algebra is a specific type of flat principal bundle on an algebraic curve. When the base field is of prime characteristic ,…
Genus formulas for dormant modular curves and asymptotic behavior of their function fields
Kohei Aoyama, Youhei Morita, Yasuhiro Wakabayashi
Towers of algebraic function fields over finite fields play a fundamental role in arithmetic geometry and coding theory. Classical examples arising from modular and Drinfeld modula…
Frobenius pull-back of parabolic bundles and dormant opers
Yasuhiro Wakabayashi
We study parabolic bundles on an algebraic curve in positive characteristic. Our motivation is to properly formulate Frobenius pull-backs of parabolic bundles in a way that extends…
Holonomic -modules of arithmetic type and middle convolution
Yasuhiro Wakabayashi
The aim of the present paper is to study arithmetic properties of -modules on an algebraic variety over the field of algebraic numbers. We first provide a framework fo…
Infinitesimal deformations of opers in positive characteristic and the de Rham cohomology of symmetric products
Yasuhiro Wakabayashi
The Eichler-Shimura isomorphism describes a certain cohomology group with coefficients in a space of polynomials by using holomorphic modular/cusp forms. It determines a canonical…