PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
May 7, 2026Canadian Mathematical Bulletin0 citationsOpen Access

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

DBDebargha BanerjeeSDSrijan Das

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.

Abstract

We compute extension groups in the category of duals of -adic Banach space representations of GL 2 (Q ).Focusing on representations arising from the -adic local Langlands correspondence for generic Galois representations, we classify these extensions completely.These results are then applied to prove the vanishing of extensions between the dual -adic Banach space representations attached to reducible Galois representations and supercuspidal Galois isotypic components of the -adic tale cohomology of the finite level Drinfeld spaces.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Banerjee et al. (2026) studied this question.

synapsesocial.com/papers/69fc2b608b49bacb8b3478b9https://doi.org/10.4153/s0008439526102021
Ask AI
Helpful
Bookmark
Share
View Full Paper