On the Eisenstein ideal of Drinfeld modular curves

2007/10/18 by Ambrus Pál, Ambrus Pal, Pal, Ambrus
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.NT #msc:11G09 #msc:11G18

paper · pdf · doi:10.48550/arxiv.0710.3569

37 pages. Final version; to appear in IJNT

arxiv created 2007/10/25 · arxiv updated 2009/12/01

Abstract

Let \goth E(\goth p) denote the Eisenstein ideal in the Hecke algebra \Bbb T(\goth p) of the Drinfeld modular curve X₀(\goth p) parameterizing Drinfeld modules of rank two over \Bbb F_q[T] of general characteristic with Hecke level \goth p-structure, where \goth p\triangleleft\Bbb F_q[T] is a non-zero prime ideal. We prove that the characteristic p of the field \Bbb F_q does not divide the order of the quotient \Bbb T(\goth p)/\goth E(\goth p) and the Eisenstein ideal \goth E(\goth p) is locally principal.

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