Vortrag
What is… an Iwasawa algebra?
Vortrag von Ana Marija Vego
Datum: 19.03.24 Zeit: 16.30 - 17.30 Raum:
''The Iwasawa algebra is a key object in the study of p-adic L-functions, which are a central topic in number theory. The Iwasawa algebra arises naturally in this context as a tool for understanding the behavior of certain arithmetic invariants, such as Selmer groups and class groups, in towers of number fields. It provides a framework for studying these invariants in a unified way over all the levels of the tower. This allows us to investigate the arithmetic properties of number fields and their associated objects, particularly in the context of p-adic L-functions and Galois representations. It has applications in various areas of number theory, including the study of special values of L-functions, the Birch and Swinnerton-Dyer conjecture, and the structure of class groups of number fields. In this talk we will introduce Iwasawa algebras and give some basic properties. We’ll then explore how these algebras are used in constructing Euler systems and obtaining p-adic L-functions. If time allows, we'll also touch on the main conjecture of Iwasawa theory.''