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Diophantine Geometry I SemesterWiSe 2024 / 25 Lecturer Walter Gubler Type of course (Veranstaltungsart) Vorlesung German title Diophantische Geometrie I Contents Diophantine Geometry is a very old and fascinating field. It deals with entire or rational solutions of polynomial equations. A famous example is Fermat's conjecture which was open for many years until Wiles solved it recently. In Diophantine Geometry I, we will introduce heights and we will prove Roth's theorem from diophantine approximation and the theorem of Mordell-Weil from the theory of abelian varieties. In diophantine geometry II, these two theorems lead to a proof of the Mordell-conjecture. We will follow Vojta's proof with simplification of Bombieri. This proof is more elementary than the original proof of Faltings for which Faltings received the Fields medal in 1986. Literature Bombieri, Gubler: Heights in Diophantine Geometry; Hindry, Silverman: Diphantine Geometry; Lang: Fundamentals of Diophantine Geometry; Serre: Lectures on the Mordell--Weil theorem. Recommended previous knowledge Algebra. For diophantine geometry II, some basic knowledge about Algebraic Geometry is needed. Time/Date Tuesday, Thursday 8-10 (Exercises Wed. 12-14) Location M103 (Exercises in M101) Registration
BV, MV, MArGeo ECTS 9 |