P-Adic families of Siegel modular cuspforms
  Let p be an odd prime and g an integer greater or equal to 2. 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 result relies on the construction of a family of sheaves of locally analytic overconvergent modular forms. 
Fabrizio Andreatta, Adrain Iovita, Vincent Pilloni
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