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Multivariable (φ, O × K )-modules and local-global compatibility

Abstract : Let p be a prime number, K a finite unramified extension of Q p and F a finite extension of F p. Using perfectoid spaces we associate to any finitedimensional continuous representation ρ of Gal(K/K) over F an étale (φ, O × K)module D ⊗ A (ρ) over a completed localization A of F O K. We conjecture that one can also associate an étale (φ, O × K)-module D A (π) to any smooth representation π of GL 2 (K) occurring in some Hecke eigenspace of the mod p cohomology of a Shimura curve, and that moreover D A (π) is isomorphic (up to twist) to D ⊗ A (ρ), where ρ is the underlying 2-dimensional representation of Gal(K/K). Using previous work of the same authors, we prove this conjecture when ρ is semi-simple and sufficiently generic.
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https://hal.archives-ouvertes.fr/hal-03840843
Contributor : Morra Stefano Connect in order to contact the contributor
Submitted on : Sunday, November 6, 2022 - 11:08:58 AM
Last modification on : Thursday, November 10, 2022 - 3:31:19 AM

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BHHMS3-ArXiV.pdf
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  • HAL Id : hal-03840843, version 1
  • ARXIV : 2211.00438

Citation

Christophe Breuil, Florian Herzig, Yongquan Hu, Stefano Morra, Benjamin Schraen. Multivariable (φ, O × K )-modules and local-global compatibility. 2022. ⟨hal-03840843⟩

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