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In the first part, we introduce theory of p-adic analysis for one variable p-adic functions and then use them to construct Kubota-Leopoldt p-adic L-functions.In the second part, we give a description of the Iwasawa modules attached to p-adic Galois representations of the absolute Galois group of K in terms of the theory of (φ,Γ)-modules of Fontaine. When the representation is de Rham when K be finite extension of Qp. This gives a natural construction of the exponential map of Perrin-Riou which is used in the construction and the study of p-adic L-functions.In the third part, we give formulas for Bloch-Kato’s exponential map and its dual for an alsolutely crystalline p-adic representation V . As a corollary of these computation, we can give a improved description of Perrin-Riou’s exponential map, which interpolates Bloch-Kato’s exponentials for the twists of V. Finally we use this map to reconstruct Kubota-Leopoldt p-adic L-functions.
Prospective Student Info Sessions
Faculty of Science Information SessionDate: Tuesday, 24 November 2020
Time: 10:00 to 11:00
UBC’s Faculty of Science is home to an array of outstanding scientists and students who strive to unravel the principles that underlie our universe - from the subatomic to the macroscopic, from pure mathematics to biotechnology, from ecosystems to galactic systems. In this session hosted by Professor Mark MacLachlan, Associate Dean of Research & Graduate Studies, we’ll hear from faculty members and graduate students on some of the exciting research happening within the Faculty of Science. We’ll also take a look at the wide range of graduate programs available, what its like to be a grad student in Science, and also provide some application advice. Be sure to join us and get an insight into how UBC Science is discovering new scientific knowledge and preparing Canada’s and the world’s next generation of scientists.