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

## Introductory Workshop: Algebraic Cycles, L-Values, and Euler Systems January 23, 2023 - January 27, 2023

**Speaker(s):**Antonio Lei (University of Ottawa)

**Location:**SLMath: Eisenbud Auditorium, Online/Virtual

**Tags/Keywords**

Perrin-Riou map

Iwasawa theory

**Primary Mathematics Subject Classification**

**Secondary Mathematics Subject Classification**

#### The Perrin-Riou Map And Its Use In Iwasawa Theory Pt II

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.

#### The Perrin-Riou Map And Its Use In Iwasawa Theory Pt II

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