Characteristic polynomials of automorphisms of hyperelliptic curves

Details Characteristic polynomials of automorphisms of hyperelliptic curves Characteristic polynomials of automorphisms of hyperelliptic curves

2008-04-03

arxiv.org/abs/0804.0578v1

pp. 101-112 in: Arithmetic, Geometry, Cryptography and Coding Theory (G. Lachaud, C. Ritzenthaler, and M. A. Tsfasman, eds.),

Mathematics

Algebraic Geometry

LaTeX, 11 pages

Scientific paper

Let alpha be an automorphism of a hyperelliptic curve C of genus g, and let alpha' be the automorphism of P^1 induced by alpha. Let n be the order of alpha and let n' be the order of alpha'. We show that the triple (g,n,n') completely determines the characteristic polynomial of the automorphism alpha^* of the Jacobian of C, unless n is even, n=n', and (2g+2)/n is even, in which case there are two possibilities. We give explicit formulas for the characteristic polynomial in all cases.

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