A note on extensions of p -adic representations of GL₂ (Qₚ)

Key Points

• This work aims to compute and classify extension groups of p-adic representations in the dual Banach space category.
• Computed extension groups in duals of p-adic Banach space representations of GL2(Qp).
• Focused on representations from p-adic local Langlands correspondence for generic Galois representations.
• Proved vanishing of extensions between specific Galois representations and supercuspidal isotypic components.
• Classified extensions completely for the dual p-adic Banach space representations.
• Showed that extensions vanish between reducible Galois representations and specific components of p-adic cohomology.
• Provided insights into the structure of extensions in the context of Drinfeld spaces.