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A note on extensions of p-adic representations of
$\mathrm {GL}_2(\mathbb {Q}_p)$
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 04 May 2026, pp. 1-13
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We compute extension groups in the category of duals of p-adic Banach space representations of
$\mathrm {GL}_2(\mathbb {Q}_p)$. Focusing on representations arising from the p-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 p-adic Banach space representations attached to reducible Galois representations and supercuspidal Galois isotypic components of the p-adic étale cohomology of the finite-level Drinfeld spaces.
