PAGE STILL UNDER CONSTRUCTIONArithmetic of Plane CurvesHHU Düsseldorf, Wintersemester 2026/27 Teacher: Jun.-Prof. Dr. Marta Pieropan
Lecture room: 2522.00.72
Content
Plane curves are subsets of the projective plane defined by homogeneous polynomials in three variables. In this course you will study the set of solutions of those homogeneous polynomials over fields that are not algebraically closed and learn about their properties. Learning objectives:
In degree 2, you will learn about plane conics, their classification un to isomorphism and their connection to central symple algebras. In degree 3, you will learn about elliptic curves, their group of points, the Mordell-Weil Theorem over the rational numbers, and the structure of the set of torsion points. In degree at least 4, you will learn about Fermat's descent and its application to prove some cases of Fermat's Last Theorem. Time permitting, we will get a glimpse about the theory behind Wile's proof of Fermat' s Last Theorem.
Exercise classesInformation about the exercise session will appear later. ExamInformation about the exam will appear soon. LiteratureGille and Szamueli, Central simple algebras and Galois cohomology, Cambridge University Press 2017 ULB link Knapp, Elliptic curves, Princeton University Press 2018. ULB link | ||