Iwasawa theory and F-analytic Lubin-Tate (φ,Γ)-modules

2015/12/10 by Laurent Berger, Berger, Laurent, Lionel Fourquaux +1
Mathematics · #11F #11S #14G #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1512.03383

openalex publication_date 2015/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a finite extension of Q_p. We use the theory of (φ,Γ)-modules in the Lubin-Tate setting to construct some corestriction-compatible families of classes in the cohomology of V, for certain representations V of Gal(Q_p/K). If in addition V is crystalline, we describe these classes explicitly using Bloch-Kato's exponential maps. This allows us to generalize Perrin-Riou's period map to the Lubin-Tate setting.

Related

• Coates-Wiles homomorphisms and Iwasawa cohomology for Lubin-Tate extensions
• Irreducible mod p Lubin-Tate (φ,Γ)-modules
• Théorie locale du corps de classes et (φ,Γ)-modules Lubin-Tate
• Rigid character groups, Lubin-Tate theory, and (φ,Γ)-modules
• Galois Cohomology for Lubin-Tate (φ_q,Γ_LT)-modules over Coefficient rings