Degree bounds for projective division fields associated to elliptic\n modules with a trivial endomorphism ring

2020/02/19 by Alina Carmen Cojocaru, Cojocaru, Alina Carmen, Nathan D. Jones +1
Mathematics · Social Sciences · #11F80 (Secondary) #11G05 #11G09 (Primary) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Historical and Political Studies #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2002.08411

openalex publication_date 2020/02/19 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Let k be a global field, let A be a Dedekind domain with \Quot(A)\n= k, and let K be a finitely generated field. Using a unified approach for\nboth elliptic curves and Drinfeld modules M defined over K and having a\ntrivial endomorphism ring, with k= \ℚ, A = \ℤ in the former\ncase and k a global function field, A its ring of functions regular away\nfrom a fixed prime in the latter case, for any nonzero ideal mathfraka lhd\nA we prove best possible estimates in the norm | mathfraka| for the\ndegrees over K of the subfields of the mathfraka-division fields of M\nfixed by scalars.\n

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