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On component groups of Jacobians of Drinfeld modular curves

Mihran Papikian — 2004

Annales de l'Institut Fourier

Let J 0 ( 𝔫 ) be the Jacobian variety of the Drinfeld modular curve X 0 ( 𝔫 ) over 𝔽 q ( t ) , where 𝔫 is an ideal in 𝔽 q [ t ] . Let 0 B J 0 ( 𝔫 ) A 0 be an exact sequence of abelian varieties. Assume B , as a subvariety of J 0 ( 𝔫 ) , is stable under the action of the Hecke algebra 𝕋 End ( J 0 ( 𝔫 ) ) . We give a criterion which is sufficient for the exactness of the induced sequence of component groups 0 Φ B , Φ J , Φ A , 0 of the Néron models of these abelian varieties over 𝔽 q [ [ 1 t ] ] . This criterion is always satisfied when either A or B is one-dimensional. Moreover, we prove that the sequence...

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