$p$-adic families of Siegel modular  cuspforms

Fabrizio Andreatta; Adrian Iovita; Vincent Pilloni

doi:https://doi.org/10.4007/annals.2015.181.2.5

Abstract

Let $p$ be an odd prime and $g\geq 2$ an integer. We prove that a finite slope Siegel cuspidal eigenform of genus $g$ can be $p$-adically deformed over the $g$-dimensional weight space. The proof of this theorem relies on the construction of a family of sheaves of locally analytic overconvergent modular forms.

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@article{PiTW, mrkey= {3097946}, author = {Pilloni, Vincent}, title = {Formes modulaires surconvergentes}, journal = {Ann.~Inst.~Fourier (Grenoble)}, fjournal = {Universit{é} de Grenoble. Annales de l'Ínstitut Fourier}, YEAR = {2013}, volume = {63}, issue = {1}, pages = {219--239}, zblnumber = {06177080}, mrnumber = {3097946}, mrclass = {11F33}, mrreviewer = {Francesc Castell\'{a}}, DOI = {10.5802/aif.2759}, }
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@misc{PiS2, author = {Bijakowski, Stéphane and Pilloni, Vincent and Stroh, B.}, title = {Classicité de formes modulaires surconvergentes}, note = {preprint}, }
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@article{SU, mrkey = {2261226}, author = {Skinner, Christopher and Urban, Eric}, title = {Sur les déformations {$p$}-adiques de certaines représentations automorphes}, journal = {J. Inst. Math. Jussieu}, fjournal = {Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Mathématiques de Jussieu}, volume = {5}, year = {2006}, number = {4}, pages = {629--698}, issn = {1474-7480}, mrclass = {11G40 (11F33 11F46 11F80 11F85)}, mrnumber = {2261226}, mrreviewer = {Neil P. Dummigan}, doi = {10.1017/S147474800600003X}, zblnumber = {1169.11314}, }
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@article{Sch, mrkey = {2114732}, author = {Schmidt, R.}, title = {Iwahori-spherical representations of {${\mathit{GSp}}(4)$} and {S}iegel modular forms of degree $2$ with square-free level}, journal = {J. Math. Soc. Japan}, volume = {57}, year = {2005}, pages = {259--293}, doi = {10.2969/jmsj/1160745825}, zblnumber = {1166.11325}, mrclass = {11F46 (11F70 11F85)}, mrreviewer = {Ramin Takloo-Bighash}, mrnumber = {2114732}, }
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@article{Str, mrkey = {2679041}, author = {Stroh, Beno{\^ı}t}, title = {Compactification de variétés de {S}iegel aux places de mauvaise réduction}, journal = {Bull. Soc. Math. France}, fjournal = {Bulletin de la Société Mathématique de France}, volume = {138}, year = {2010}, number = {2}, pages = {259--315}, issn = {0037-9484}, coden = {BSMFAA}, mrclass = {14K10 (14G35 14M27)}, mrnumber = {2679041}, mrreviewer = {Rolf Berndt}, zblnumber = {1203.14048}, }
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@article{Ur, mrkey = {2846490}, author = {Urban, Eric}, title = {Eigenvarieties for reductive groups}, journal = {Ann. of Math.}, fjournal = {Annals of Mathematics. Second Series}, volume = {174}, year = {2011}, number = {3}, pages = {1685--1784}, issn = {0003-486X}, coden = {ANMAAH}, mrclass = {22E55 (11F75 11F85)}, mrnumber = {2846490}, mrreviewer = {Neven Grbac}, doi = {10.4007/annals.2011.174.3.7}, zblnumber = {1285.11081}, }

$p$-adic families of Siegel modular cuspforms

Abstract

Authors