For an odd prime p, we construct some admissible Banach representations of GL2.(ℚp) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti-Tate representations of Gal(ℚp/ℚp) via the p-adic local Langlands correspondence. To achieve this, we generalize Breuil’s work in the semistable case and work on the first covering of the Drinfel;d upper half-plane. Our main tool is an explicit semistable model of the first covering.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Drinfel’d upper half-plane
- p-adic local Langlands correspondence of GL(ℚ)