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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Simple ${\mathcal L}$-invariants for GL$_n$
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by Yiwen Ding PDF
Trans. Amer. Math. Soc. 372 (2019), 7993-8042 Request permission

Abstract:

Let $L$ be a finite extension of ${\mathbb Q}_p$, and $\rho _L$ be an $n$-dimensional semistable noncrystalline $p$-adic representation of ${\mathrm {Gal}}_L$ with full monodromy rank. Via a study of Breuil’s (simple) ${\mathcal L}$-invariants, we attach to $\rho _L$ a locally ${\mathbb Q}_p$-analytic representation $\Pi (\rho _L)$ of ${\mathrm {GL}}_n(L)$, which carries the exact information of the Fontaine–Mazur simple ${\mathcal L}$-invariants of $\rho _L$. When $\rho _L$ comes from an automorphic representation of $G({\mathbb A}_{F^+})$ (for a unitary group $G$ over a totally real field $F^+$ which is compact at infinite places and ${\mathrm {GL}}_n$ at $p$-adic places), we prove under mild hypothesis that $\Pi (\rho _L)$ is a subrepresentation of the associated Hecke-isotypic subspaces of the Banach spaces of $p$-adic automorphic forms on $G({\mathbb A}_{F^+})$. In other words, we prove the equality of Breuil’s simple ${\mathcal L}$-invariants and Fontaine–Mazur simple $L$-invariants.
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Additional Information
  • Yiwen Ding
  • Affiliation: BICMR, Peking University, 5 Yiheyuan Road, Haidian District, Beijing 100871, People’s Republic of China
  • MR Author ID: 984199
  • Email: yiwen.ding@bicmr.pku.edu.cn
  • Received by editor(s): August 31, 2018
  • Received by editor(s) in revised form: March 4, 2019
  • Published electronically: July 2, 2019
  • Additional Notes: This work was supported by EPSRC Grant No. EP/L025485/1 and by Grant No. 8102600240 from BICMR
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7993-8042
  • MSC (2010): Primary 11S80; Secondary 22D12
  • DOI: https://doi.org/10.1090/tran/7859
  • MathSciNet review: 4029688