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  • Cited by 5
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Johansson, Christian 2016. A trace formula approach to control theorems for overconvergent automorphic forms. Manuscripta Mathematica,


    Andreatta, Fabrizio Iovita, Adrian and Pilloni, Vincent 2015. p-adic families of Siegel modular cuspforms. Annals of Mathematics, p. 623.


    Johansson, Christian 2013. Classicality for small slope overconvergent automorphic forms on some compact PEL Shimura varieties of type C. Mathematische Annalen, Vol. 357, Issue. 1, p. 51.


    Pilloni, Vincent 2012. Modularité, formes de Siegel et surfaces abéliennes. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2012, Issue. 666,


    Hida, Haruzo 2010. The Iwasawaμ-invariant ofp-adic HeckeL-functions. Annals of Mathematics, Vol. 172, Issue. 1, p. 41.


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  • Journal of the Institute of Mathematics of Jussieu, Volume 1, Issue 1
  • January 2002, pp. 1-76

CONTROL THEOREMS OF COHERENT SHEAVES ON SHIMURA VARIETIES OF PEL TYPE

  • Haruzo Hida (a1)
  • DOI: http://dx.doi.org/10.1017/S1474748002000014
  • Published online: 01 January 2003
Abstract

An exact control theorem is proven for nearly ordinary $p$-adic automorphic forms on symplectic and unitary groups over totally real fields if the algebraic group is split at $p$. In particular, a given nearly ordinary holomorphic Hecke eigenform can be lifted to a family of holomorphic Hecke eigenforms indexed by weights of the standard maximal split torus of the group. Their $q$-expansion coefficients are Iwasawa functions on the Iwasawa algebra of ${\mathbb{Z}}_p$-points of the split torus. The method is applicable to any reductive algebraic groups yielding Shimura varieties of PEL type under mild assumptions on the existence of integral toroidal compactification of the variety. Even in the Hilbert modular case, the result contains something new: freeness of the universal nearly ordinary Hecke algebra over the Iwasawa algebra, which eluded my scrutiny when I studied general theory of the $p$-adic Hecke algebra in the 1980s.

AMS 2000 Mathematics subject classification: Primary 11F03; 11F30; 11F33; 11F41; 11F60; 11G15; 11G18

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Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
  • URL: /core/journals/journal-of-the-institute-of-mathematics-of-jussieu
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