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Block decompositions in the p-adic Langlands correspondence
Abstract
Let K/Qp be a finite extension, bG a connected reductive group over K, and set G = bG(K), considered as a p-adic Lie group. We show first that the Bernstein center cCG of the category of solid locally Qp-analytic representations of G is isomorphic to the center of the locally analytic distribution algebra Dla(G). We then consider the Emerton-Gee stack frXn,K of rank-n (vphi,Γ)-modules over the Robba ring for K and determine its connected components. The latter are in canonical bijection with the primitive idempotents of the ring cCGLn(K). Moreover, under the assumption that the ring of global functions on frXn,K has no non-zero locally nilpotent elements, we show that this ring is isomorphic to a Fréchet completion of cCGLn(K).
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BibTeX
@misc{le2026block,
title = {{Block decompositions in the p-adic Langlands correspondence}},
author = {Daniel Le and Matthias Strauch and Zichuan Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07648},
eprint = {2610.07648},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07648},
}
RIS
TY - UNPB
TI - Block decompositions in the p-adic Langlands correspondence
AU - Daniel Le
AU - Matthias Strauch
AU - Zichuan Wang
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.07648
UR - https://arxiv.org/abs/2610.07648
AB - Let K/Qp be a finite extension, bG a connected reductive group over K, and set G = bG(K), considered as a p-adic Lie group. We show first that the Bernstein center cC_G of the category of solid locally Qp-analytic representations of G is isomorphic to the center of the locally analytic distribution algebra D^la(G). We then consider the Emerton-Gee stack frX_n,K of rank-n (vphi,Γ)-modules over the Robba ring for K and determine its connected components. The latter are in canonical bijection with the primitive idempotents of the ring cC_GL_n(K). Moreover, under the assumption that the ring of global functions on frX_n,K has no non-zero locally nilpotent elements, we show that this ring is isomorphic to a Fréchet completion of cC_GL_n(K).
ER -