Computing endomorphism rings and Frobenius matrices of Drinfeld modules

JOURNAL OF NUMBER THEORY

卷:237

Article

Garai, Sumita¹  Papikian, Mihran¹ 

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

关键词: Drinfeld modules;    Endomorphism rings;    Gorenstein rings;   

DOI  :  10.1016/j.jnt.2019.11.018

来源: Elsevier

【 摘 要 】

Let F-q[T] be the polynomial ring over a finite field F-q. We study the endomorphism rings of Drinfeld F-q[T]-modules of arbitrary rank over finite fields. We compare the endomorphism rings to their subrings generated by the Frobenius endomorphism and deduce from this a refinement of a reciprocity law for division fields of Drinfeld modules proved in our earlier paper. We then use these results to give an efficient algorithm for computing the endomorphism rings and discuss some interesting examples produced by our algorithm. (c) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free