Regularity of quotients of Drinfeld modular schemes

Let $A$ be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal $I \subset A$, Drinfeld defined the notion of structure of level $I$ on a Drinfeld module. We extend this to that of level $N$, where $N$ is a finitely generated torsion $A$-module. The case where $N=(I^{-1}/A)^d$, where $d$ is the rank of the Drinfeld module,coincides with the structure of level $I$. The moduli functor is representable by a regular affine scheme. The automorphism group $\mathrm{Aut}_{A}(N)$ acts on the moduli space. Our theorem gives a class of subgroups for which the quotient of the moduli scheme is regular. Examples include generalizations of $\Gamma_0$ and of $\Gamma_1$. We also show that parabolic subgroups appearing in the definition of Hecke correspondences are such subgroups

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筑波大学University of Tsukuba博士（工学）Doctor of Philosophy in Engineering2000【要旨】thesi

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この論文は国立情報学研究所の学術雑誌公開支援事業により電子化されました