The growth of the discriminant of the endomorphism ring of the reduction of a rank 2 generic Drinfeld module

Alina Carmen Cojocaru, Mihran Papikian

Research output: Contribution to journalArticlepeer-review

Abstract

For q an odd prime power, A=Fq[T], and F=Fq(T), let ψ:A→F{τ} be a Drinfeld A-module over F of rank 2 and without complex multiplication, and let p=pA be a prime of A of good reduction for ψ, with residue field Fp. We study the growth of the absolute value |Δp| of the discriminant of the Fp-endomorphism ring of the reduction of ψ modulo p and prove that, for all p, |Δp| grows with |p|. Moreover, we prove that, for a density 1 of primes p, |Δp| is as close as possible to its upper bound |ap2−4μpp|, where X2+apX+μpp∈A[X] is the characteristic polynomial of τdegp.

Original languageEnglish (US)
JournalJournal of Number Theory
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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