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Oberseminar SoSe 2010 Zusammenfassung des Vortrags von T. Shioda (Rikkyo/RIMS, JAP)

Galois representations and Mordell-Weil lattices

I discuss Galois representations and algebraic equations which arise from Mordell-Weil lattices in a very natural way. Starting from a general setting, we focus on the case of rational elliptic surfaces, especially of exceptional type E6, E7 and E8. We hope to treat both "big Galois" and "small Galois" problems in some detail, and to present some old and new explicit examples. with applications to number theory and classical geometry (e.g. 27 lines on a cubic surface).