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- W4287865539 abstract "Let $psi: A to F{tau}$ be a Drinfeld $A$-module over $F$ of rank 2 and without complex multiplication, where $A = {mathbb{F}}_q[T]$, $F = {mathbb{F}}_q(T)$, and $q$ is an odd prime power. For a prime $mathfrak{p} = p A$ of $A$ of good reduction for $psi$ and with residue field ${mathbb{F}}_{mathfrak{p}}$, we study the growth of the absolute value $|Delta_{mathfrak{p}}|$ of the discriminant of the ${mathbb{F}}_{mathfrak{p}}$-endomorphism ring of the reduction of $psi$ modulo $mathfrak{p}$. We prove that for all $mathfrak{p}$, $|Delta_{mathfrak{p}}|$ grows with $|p|$. Moreover, we prove that for a density 1 of primes $mathfrak{p}$, $|Delta_{mathfrak{p}}|$ is as close as possible to its upper bound $|a_{mathfrak{p}}^2 - 4 mu_{mathfrak{p}}p|$, where $X^2+a_{mathfrak{p}}X+mu_{mathfrak{p}} p in A[X]$ is the characteristic polynomial of $tau^{text{deg} p}$." @default.
- W4287865539 created "2022-07-26" @default.
- W4287865539 creator A5021892978 @default.
- W4287865539 creator A5025870478 @default.
- W4287865539 date "2020-02-21" @default.
- W4287865539 modified "2023-09-29" @default.
- W4287865539 title "The growth of the discriminant of the endomorphism ring of the reduction of a rank 2 generic Drinfeld module" @default.
- W4287865539 doi "https://doi.org/10.48550/arxiv.2002.09582" @default.
- W4287865539 hasPublicationYear "2020" @default.
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