Gross'Conjecture for Extensions Ramified over Three Points of $\Bbb P^1$

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概要

• 論文の詳細を見る

• B. Gross has formulated a conjectural generalization of the class number formula. Suppose $L/K$ is an abelian extension of global fields with Galois group $G$. A generalized Stickelberger element $θ \in \ZZ[G]$ is constructed from special values of $L$-functions at $s = 0$. Gross'conjecture then predicts some $I$-adic information about $θ$, where $I \subseteq \ZZ[G]$ is the augmentation ideal. In this paper, we prove (under a mild hypothesis) the conjecture for the maximal abelian extension of the rational function field $\FF_q(X)$ that is unramified outside a set of three degree $1$ places.

• 東京大学の論文

著者

• Reid Michael

  Department Of Anthropology University Of Toronto

• Reid Michael

  Department Of Mathematics University Of Arizona

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