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Component group of thep-new subvariety ofJ 0(M p )

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Abstract

For an abelian varietyA over ℚ p , the special fibre in the Néron model ofA over ℤ p is the extension of a finite group scheme over ℤ p , called the group of connected components, by the connected component of identity. WhenA is the Jacobian variety of an algebraic curve, its component group has been calculated in many cases. We determine in this paper the component group of thep-new subvariety ofJ 0(M p ), forM>1 a positive integer andp≥5 a prime not dividingM. Such a subvariety is not the Jacobian of any obvious curve, but it is not clear if it can ever be realised as the Jacobian of a curve.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 117543, Singapore

    San Ling

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  1. San Ling
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Correspondence to San Ling.

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Ling, S. Component group of thep-new subvariety ofJ 0(M p ). Isr. J. Math. 116, 117–123 (2000). https://doi.org/10.1007/BF02773215

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  • DOI: https://doi.org/10.1007/BF02773215

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