p-adic families of Siegel modular cuspforms

By F. Andreatta, Adrain Iovita, V. Pilloni. 2012

91 citations recorded by the source corpus.

Let p be an odd prime and g 2 an integer. We prove that a nite 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. Contents

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/feb901fa23a55aecdd29fe9a0dc8de981408e3fa

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In Geometry and Topology

1. J. Thorne
2. Michael Harris
3. Richard Taylor
4. T. Gee
5. Peter Scholze
6. Kai-Wen Lan
7. X. Wan
8. David Geraghty

In Mathematical Physics

1. J. Thorne
2. Michael Harris
3. Richard Taylor
4. T. Gee
5. Peter Scholze
6. Kai-Wen Lan
7. X. Wan
8. David Geraghty

Citations in the corpus

• Iwasawa Main Conjecture for Supersingular Elliptic Curves (2014, background): “This can be achieved by applying the result in [45], and the construction for unitary group is done in [46].”
• On the rigid cohomology of certain Shimura varieties (2014, background): “This observation seems to have been made independently, at about the same time, by Andreatta, Iovita and Pilloni (see [1,2]).”