Abelian surfaces over finite fields as Jacobians. With an appendix by Everett W. Howe.
Formal group laws for certain formal groups arising from modular curves
The formal completion of the Néron model of J(p).
For any prime number p > 3 we compute the formal completion of the Néron model of J(p) in terms of the action of the Hecke algebra on the Z-module of all cusp forms (of weight 2 with respect to Γ(p)) with integral Fourier development at infinity.
Formal groups and L-series.
Modular invariant and good reduction of elliptic curves.
Okutsu invariants and Newton polygons
Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a -adic factorization method based on Newton polygons of higher order. The running-time and memory requirements of the algorithm appear to be very good.
Jacobians in isogeny classes of abelian surfaces over finite fields
We give a complete answer to the question of which polynomials occur as the characteristic polynomials of Frobenius for genus- curves over finite fields.
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