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Algebraic Geometry

Course Code :2001WETAAG
Study domain:Mathematics
Academic year:2019-2020
Semester:1st semester
Contact hours:60
Credits:6
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:Dutch
Exam period:exam in the 1st semester
Lecturer(s)Lieven Le Bruyn

3. Course contents *

Algebraic geometry allows us to use geometric insight to understand algebraic theories such as number theory. We will introduce the prime spectrum and its structure sheaf, and study etale extensions which are analogous to covers of manifolds. This gives us a method to introduce the etale fundamental group. As an application we show that prime numbers correspond geometrically to knots and that number theoretic reciprocity laws correspond to the linking behaviour of these knots.