Drinfeld Modules, Frobenius Endomorphisms, and CM-Liftings

Alina Carmen Cojocaru; Mihran Papikian

doi:10.1093/imrn/rnu178

Drinfeld Modules, Frobenius Endomorphisms, and CM-Liftings

Alina Carmen Cojocaru, Mihran Papikian

Mathematics

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8 Scopus citations

Abstract

We give a global description of the Frobenius elements in the division fields of Drinfeld modules of rank 2. We apply this description to derive a criterion for the splitting modulo primes of a class of nonsolvable polynomials, and to study the frequency with which the reductions of Drinfeld modules have small endomorphism rings. We also generalize some of these results to higher rank Drinfeld modules and prove CM-lifting theorems for Drinfeld modules.

Original language	English (US)
Pages (from-to)	7787-7825
Number of pages	39
Journal	International Mathematics Research Notices
Volume	2015
Issue number	17
DOIs	https://doi.org/10.1093/imrn/rnu178
State	Published - 2015

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnu178

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abstract = "We give a global description of the Frobenius elements in the division fields of Drinfeld modules of rank 2. We apply this description to derive a criterion for the splitting modulo primes of a class of nonsolvable polynomials, and to study the frequency with which the reductions of Drinfeld modules have small endomorphism rings. We also generalize some of these results to higher rank Drinfeld modules and prove CM-lifting theorems for Drinfeld modules.",

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AB - We give a global description of the Frobenius elements in the division fields of Drinfeld modules of rank 2. We apply this description to derive a criterion for the splitting modulo primes of a class of nonsolvable polynomials, and to study the frequency with which the reductions of Drinfeld modules have small endomorphism rings. We also generalize some of these results to higher rank Drinfeld modules and prove CM-lifting theorems for Drinfeld modules.

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Drinfeld Modules, Frobenius Endomorphisms, and CM-Liftings

Abstract

All Science Journal Classification (ASJC) codes

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