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NON-SEMI-STABLE LOCI IN HECKE STACKS AND FARGUES’ CONJECTURE
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- Journal:
- Journal of the Institute of Mathematics of Jussieu , First View
- Published online by Cambridge University Press:
- 23 October 2025, pp. 1-31
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We show the Harris–Viehmann conjecture under some Hodge–Newton reducibility condition for a generalisation of the diamond of a non-basic Rapoport–Zink space at infinite level, which appears as a cover of the non-semi-stable locus in the Hecke stack. We show also that the cohomology of the non-semi-stable locus with coefficients coming from a cuspidal Langlands parameter vanishes. As an application, we show the Hecke eigensheaf property in Fargues’ conjecture for cuspidal Langlands parameters in the
$ {\mathrm {GL}}_2$-case.
