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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.17469 |
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Table of Contents:
- For a $p$-adic field $F$ of residual cardinality $q$, we provide a triangulated equivalence between the bounded derived category $D^b(\mathcal{B}_{1}(G)_{fg})$ of finitely generated unipotent representations of $G=\mathrm{GL}_2(F)$ and perfect complexes over a dg enriched Schur algebra, in the non-banal case of odd characteristic $l$ dividing $q+1$. The dg Schur algebra is the dg endomorphism algebra of a projective resolution of a direct sum $V$ of the parahoric inductions of the trivial representations of the reductive quotients of $G$, and $V$ is shown to be a classical generator of $D^b(\mathcal{B}_{1}(G)_{fg})$.