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Complete p-Descent for Jacobians of Hermitian Curves

Published online by Cambridge University Press:  04 December 2007

NEIL DUMMIGAN
NEIL DUMMIGAN
Affiliation:
Merton College, Oxford OX1 4JD, U.K.
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Abstract

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Let X be the Fermat curve of degree q+1 over the field k of q$^2$ elements, where q is some prime power. Considering the Jacobian J of X as a constant abelian variety over the function field k(X), we calculate the multiplicities, in subfactors of the Shafarevich–Tate group, of representations associated with the action on X of a finite unitary group. J is isogenous to a power of a supersingular elliptic curve E, the structure of whose Shafarevich–Tate group is also described.

Keywords

fermat curveabelian varietydescentcrystalline cohomologyfinite unitary group.
Type
Research Article
Information
Compositio Mathematica , Volume 119 , Issue 2 , November 1999 , pp. 111 - 132
Copyright
© 1999 Kluwer Academic Publishers