Adèles and the geometry of schemes

Event details
Date | 22.09.2015 |
Hour | 15:15 › 17:00 |
Speaker | Michael Groechenig, (Imperial College) |
Location | |
Category | Conferences - Seminars |
The ring of adèles plays a fundamental role in number theory. Our current understanding of class field theory, and its far-reaching extension, the Langlands Programme, would be inconceivable without it. It is a bridge connecting local and global aspects.
There is a similar approach to the geometry of varieties. In the first part of my talk I will survey how classical results for algebraic curves can be obtained adelically. We will use this to observe an analogy between Serre duality and Autoduality of Jacobians. We conclude this part by studying Weil’s adelic uniformization for G-bundles on curves.
In the second part we will discuss a generalisation of Weil’s result general varieties and perfect complexes. As a corollary we obtain that Noetherian schemes can be reconstructed from Beilinson’s cosimplicial ring of adèles.
There is a similar approach to the geometry of varieties. In the first part of my talk I will survey how classical results for algebraic curves can be obtained adelically. We will use this to observe an analogy between Serre duality and Autoduality of Jacobians. We conclude this part by studying Weil’s adelic uniformization for G-bundles on curves.
In the second part we will discuss a generalisation of Weil’s result general varieties and perfect complexes. As a corollary we obtain that Noetherian schemes can be reconstructed from Beilinson’s cosimplicial ring of adèles.
Practical information
- Informed public
- Free