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## Errata for my thesis

• Page 16, "Since sigma(I[delta])=I[delta] and sigma(phi)=phi ..." - This is only true if sigma acts by permutation on {Z,...,Z[n]}. Therefore, the Galois-action on K[X,Z,...,Z[n]] is not the trivial one but the one which permutes Z,...,Z[n] in exactly the same way as it permutes {t,...,t[n]}.
• Page 17, Theorem 3.1.1, should be "is of genus 1+m^(n-2)(n(m-1)/2-m)", just as on page 14. (thanks to F. Oort, 06/10/99)
• Page 21, Table 3.2. As Johnny Edwards found, the complete set of parametrizations modulo SL(2,Z_{2,3})-equivalence for x^4+y^3=z^2 as given by Zagier in [Beukers, 1995], is not complete modulo SL(2,Z)-equivalence. The parametrization +-x = 2^3(s^2-3t^2)(s^4+18s^2t^2+9t^4), y=-2^4(s^2+2st+3t^2)(s^2-2st+3t^2)(s^2+6st+3t^2)(s^2-6st+3t^2), +-z=2^6*4st(s^2+3t^2)(3s^4-2s^2t^2+3t^4)(s^4-6s^2t^2+81t^4) is needed to hit (-7,15,76). The weighted projectively equivalent (-2^3*7,2^4*15,2^6*76) is parametrized by the first parametrization in Table 3.2.

The ramifications for the proof of Theorem 1.3.3 are minimal, since it can be easily checked that the genus 2 curves y^2=2^3(x^2-3)(x^4+18x^2+9) and y^2=-2^3(x^2-3)(x^4+18x^2+9) have no points locally at 2 or 3.

• Page 55, Proposition 4.8.18, should read "X(P) in {-1}". (thanks to Wilfrid Ivorra, 19/03/01)
• Page 60, "group of automorphisms" - should be "finite group of automorphisms".
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