2020/09/05 by Sedric Nkotto Nkung Assong, Assong, Sedric Nkotto Nkung
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2009.02533
openalex publication_date 2020/09/05 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
When travelling from the number fields theory to the function fields theory,\none cannot miss the deep analogy between rank 1 Drinfeld modules and the group\nof root of unity and the analogy between rank 2 Drinfeld modules and elliptic\ncurves. But so far, there is no known structure in number fields theory that is\nanalogous to the Drinfeld modules of higher rank r > 2. In this paper we\ninvestigate the classes of those Drinfeld modules of higher rank r > 2. We\ndescribe explicitly the Weil polynomials defining the isogeny classes of rank r\nDrinfeld modules for any rank r > 2. our explicit description of the Weil\npolynomials depends heavily on Yu's classification of isogeny classes (analogue\nof Honda-Tate at abelian varieties). Actually Yu has also explicitly did that\nwork for r = 2. To complete the classification, we define the new notion of\nfine isomorphy invariants for any rank r Drinfeld module and we prove that the\nfine isomorphy invariants together with J-invariants completely determine the\nL-isomorphism classes of rank r Drinfeld modules defined over the finite field\nL.\n