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26001 results in Abstract analysis

Page 193 of 1301

  • LOCALLY ANALYTIC VECTORS AND OVERCONVERGENT $(\unicode[STIX]{x1D711},\unicode[STIX]{x1D70F})$-MODULES

  • Part of
  • Hui Gao, Léo Poyeton
  • Journal:
    Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 1 / January 2021
    Published online by Cambridge University Press:
    03 May 2019, pp. 137-185
    Print publication:
    January 2021

  • Let $p$ be a prime, let $K$ be a complete discrete valuation field of characteristic $0$ with a perfect residue field of characteristic $p$, and let $G_{K}$ be the Galois group. Let $\unicode[STIX]{x1D70B}$ be a fixed uniformizer of $K$, let $K_{\infty }$ be the extension by adjoining to $K$ a system of compatible $p^{n}$th roots of $\unicode[STIX]{x1D70B}$ for all $n$, and let $L$ be the Galois closure of $K_{\infty }$. Using these field extensions, Caruso constructs the $(\unicode[STIX]{x1D711},\unicode[STIX]{x1D70F})$-modules, which classify $p$-adic Galois representations of $G_{K}$. In this paper, we study locally analytic vectors in some period rings with respect to the $p$-adic Lie group $\operatorname{Gal}(L/K)$, in the spirit of the work by Berger and Colmez. Using these locally analytic vectors, and using the classical overconvergent $(\unicode[STIX]{x1D711},\unicode[STIX]{x1D6E4})$-modules, we can establish the overconvergence property of the $(\unicode[STIX]{x1D711},\unicode[STIX]{x1D70F})$-modules.

  • Systematic derivation of a surface polarisation model for planar perovskite solar cells – CORRIGENDUM

  • N. E. COURTIER, J. M. FOSTER, S. E. J. O’KANE, A. B. WALKER, G. RICHARDSON
  • Journal:
    European Journal of Applied Mathematics / Volume 31 / Issue 1 / February 2020
    Published online by Cambridge University Press:
    03 May 2019, pp. 183-184
    • Article
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  • Following publication, errors were discovered in the y-axis labels of the electron and hole concentration plots in the following figure panels: figure 4c, figure 4d, figure 5c, figure 5d, figure 6c, figure 6d, figure 8c and figure 8d. The error does not affect the description, analysis or conclusions. The correct representation of the figure panels are shown here.

Page 193 of 1301