The A-module structure induced by a Drinfeld A-module of rank 2 over a finite field

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• 作者：Mohamed-Saadbouh Mohamed-Ahmed
• 关键词：Clifford analysis ; Superspace ; Dirac operator ; Radial algebra
• 刊名：Comptes Rendus Mathematique
• 出版年：2008
• 出版时间：March 2008
• 年：2008
• 卷：346
• 期：5-6
• 页码：305-308
• 全文大小：123 K

文摘

Let F_q be a finite field and let L/F_q be a finite extension. Let F be the Frobenius of L () and let (P) be the F[T]-characteristic of F. Let m be the degree of the extension L/F_q[T]/(P). There exists then cF_q[T] and μF_q such that the characteristic polynomial P_F of F is equal to P_F(X)=X²−cX+μP^m. Our main result is an analogue of Deuring's Theorem on elliptic curves: let , where i₁ and 741361731229e5d7ed518400bd7f01"" title=""Click to view the MathML source"">i₂ are two polynomials of F_q[T] such that i₂|i₁ and i₂|(c−2), there exists an ordinary Drinfeld F_q[T]-module Φ of rank 2 over L such that the structure of the finite F_q[T]-module L^Φ induced by Φ over L is isomorphic to M. To cite this article: M.-S. Mohamed-Ahmed, C. R. Acad. Sci. Paris, Ser. I 346 (2008).