Overview of Some Iwasawa Theory

Abstract

AbstractThese are the notes to the lectures giving a rather quick and dense overview of Iwasawa theory. They include the discussion of the case of the variation of the class group in \(\mathbb{Z}_{p}\)-extensions and the case of elliptic curves. For both, we give a description of the basic results and reach a formulation of the main conjecture. Furthermore a sketch of the leading term formula for the characteristic series for an elliptic curve, a hint at generalisations to other p-adic Galois representations and a vague overview of Kato’s Euler system are also included.KeywordsModular FormElliptic CurveElliptic CurfGalois GroupEuler SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.