Bloch and Kato's exponential map: three explicit formulas

By Laurent Berger. 2002

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The purpose of this article is to give formulas for Bloch-Kato's exponential map and its dual for an absolutely crystalline p-adic representation V, in terms of the (phi,Gamma)-module associated to that representation. As a corollary of these computations, we can give a very simple (and slightly improved) description of Perrin-Riou's exponential map (which interpolates Bloch-Kato's exponentials for V(k)). This new description directly implies Perrin-Riou's reciprocity formula.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3f6eea4e4cb3026964eb2ed692911ffca6868432

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Citations in the corpus

• On the Equivariant Tamagawa Number Conjecture for Tate Motives, Part II. (2006, methodology): “(We are grateful to Laurent Berger for pointing out that the methods of [ 3 ] show that the diagram (28) commutes even in the case p = 2.) Now for f = β∞ N0 = ξN0(1 + X) this formula gives”