On the Eisenstein ideal over function fields

Mihran Papikian; Fu Tsun Wei

doi:10.1016/j.jnt.2015.04.001

On the Eisenstein ideal over function fields

Mihran Papikian, Fu Tsun Wei

Mathematics

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4 Scopus citations

Abstract

We study the Eisenstein ideal of Drinfeld modular curves of small levels, and the relation of the Eisenstein ideal to the cuspidal divisor group and the component groups of Jacobians of Drinfeld modular curves. We prove that the characteristic of the function field is an Eisenstein prime number when the level is an arbitrary non-square-free ideal of Fq[T] not equal to a square of a prime.

Original language	English (US)
Pages (from-to)	384-434
Number of pages	51
Journal	Journal of Number Theory
Volume	161
DOIs	https://doi.org/10.1016/j.jnt.2015.04.001
State	Published - Oct 7 2014

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2015.04.001

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abstract = "We study the Eisenstein ideal of Drinfeld modular curves of small levels, and the relation of the Eisenstein ideal to the cuspidal divisor group and the component groups of Jacobians of Drinfeld modular curves. We prove that the characteristic of the function field is an Eisenstein prime number when the level is an arbitrary non-square-free ideal of Fq[T] not equal to a square of a prime.",

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AB - We study the Eisenstein ideal of Drinfeld modular curves of small levels, and the relation of the Eisenstein ideal to the cuspidal divisor group and the component groups of Jacobians of Drinfeld modular curves. We prove that the characteristic of the function field is an Eisenstein prime number when the level is an arbitrary non-square-free ideal of Fq[T] not equal to a square of a prime.

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JO - Journal of Number Theory

JF - Journal of Number Theory

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On the Eisenstein ideal over function fields

Abstract

All Science Journal Classification (ASJC) codes

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