Abstract: The Riemann-Roch Theorem (RRT) is the name commonly given to either of two formally analogous results in the areas of complex analysis and algebraic geometry respectively, each of which yields a formula for the dimension of certain spaces of functions with "prescribed poles" on the geometric object at hand. Our main goal is to give an “adelic proof” of the algebraic RRT, following the treatments of Iwasawa and Weil, and use it as motivation for the complex-analytic RRT, whose proof we shall only sketch. Finally, in the last section we shall present a well-known application of number-theoretic significance.
A number Theorist's Guide to the Riemann-Roch Theorem
07.11.2017 10:00 - 11:30
Organiser:
H. Hauser
Location: