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Diophantine Geometry I SemesterWiSe 2019 / 20 Lecturer Walter Gubler Type of course (Veranstaltungsart) Vorlesung 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. We strongly recommend to take simultaneously the course Algebraic Geometry I. Time/Date Di, Do: 8-10 Location Di M101, Do M103 Registration
BV, MV, MArGeo ECTS 9 |