Component group of the p-new subvariety of J0(Mp)

Abstract

For an abelian variety A over ℚp, the special fibre in the Néron model of A over ℤp is the extension of a finite group scheme over double-struck F signp, called the group of connected components, by the connected component of identity. When A 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 the p-new subvariety of J0(Mp), for M > 1 a positive integer and p ≥ 5 a prime not dividing M. 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.