ε-isomorphisms for rank one (φ, Γ)-modules over Lubin-Tate Robba rings - Malčić, Milan; Steingart, Rustam; Venjakob, Otmar; Witzelsperger, Max (Journal of the Institute of Mathematics of Jussieu, 2025)
Inspired by Nakamura's work [36] on epsilon -isomorphisms for (phi, Gamma-modules over (relative) Robba rings with respect to the cyclotomic theory, we formulate an analogous conjecture for L-analytic Lubin-Tate (phi(L), Gamma(L)-modules over (relative) Robba rings for any finite extension L of Q(p). In contrast to Kato's and Nakamura's setting, our conjecture involves L-analytic cohomology instead of continuous cohomology within the generalized Herr complex. Similarly, we restrict to the identity components of D-cris and D-dR, respectively. For rank one modules of the above type or slightly more generally for trianguline ones, we construct epsilon-isomorphisms for their Lubin-Tate deformations satisfying the desired interpolation property.