The Perrin-Riou Map and its Use in Iwasawa Theory Pt I

Perrin-Riou's big logarithm map plays an important role in Iwasawa theory. It sends systems of local Galois cohomology clases to p-adic analytic functions. In particular, it allows us to convert an Euler systems to a p-adic L-function, which is often the first step towards studying Iwasawa main conjectures. I will first review the original construction of this map developed by Perrin-Riou and its generalizations. I will then discuss how this map is used in studying Iwasawa theory in several concrete settings.

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