Number Theory Seminar
Speaker: Riccardo Pengo (KU).
Title: An adelic description of modular curves.
Title: An adelic description of modular curves.
Abstract: The aim of this talk will be to survey the relationships between modular curves and the ring of adèles of the rational numbers. The first ones are moduli spaces of elliptic curves with a prescribed torsion structure, which play a key role in the study of modular forms and in the proof of the modularity theorem. On the other hand the ring of adèles is a really algebraic object aiming to put together all the possible completions of a global field, which is used in many different contexts: class field theory, local-global principles, automorphic forms. We will see how affine modular curves can be described using adèles and we will explain our attempt to generalize this construction to different compactified versions of modular curves.
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