On Perrin-Riou's exponential map for (φ, Γ)-modules

2016/09/20 by Riedel, Andreas
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1609.06067

Abstract

Let K / ℚ_p be a finite Galois extension and D a (φ, Γ)-module over the Robba-ring B^†_\textrmrig, K. We give a generalization of the Bloch-Kato exponential map for D using continuous Galois-cohomology groups Hⁱ(G_K, W(D)) for the B-pair W(D) associated to D. We construct a big exponential map Ω_D,h (h ∈ ℕ) for cyclotomic extensions of K for D in the style of Perrin-Riou using the theory of Berger's B-pairs, which interpolates the generalized Bloch-Kato exponential maps on the finite levels.

Related

• Iwasawa theory of de Rham (ϕ,Γ)-modules over the Robba rings
• Locally analytic vectors and Z_p-extensions
• A generalization of Kato's local epsilon-conjecture for (phi,Gamma)-modules over the Robba ring
• Coates-Wiles homomorphisms and Iwasawa cohomology for Lubin-Tate extensions
• Families of Galois representations and (φ, τ)-modules