On the Eisenstein ideal of Drinfeld modular curves

Details On the Eisenstein ideal of Drinfeld modular curves On the Eisenstein ideal of Drinfeld modular curves

2007-10-18

arxiv.org/abs/0710.3569v2

Mathematics

Number Theory

37 pages. Final version; to appear in IJNT

Scientific paper

Let $\goth E(\goth p)$ denote the Eisenstein ideal in the Hecke algebra $\Bbb T(\goth p)$ of the Drinfeld modular curve $X_0(\goth p)$ 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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