Rendiconti del Seminario Matematico della Università di Padova

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Volume 132, 2014, pp. 83–102
DOI: 10.4171/RSMUP/132-7

Perverse sheaves on semiabelian varieties

Thomas Krämer[1]

(1) Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128, Palaiseau CEDEX, France

We give a Tannakian description for the category of perverse sheaves on semiabelian varieties. Our construction is based on a vanishing theorem for the hypercohomology of perverse sheaves and extends earlier results for tori and abelian varieties. As an application we explain how perverse sheaves on abelian varieties can be studied in terms of semiabelian degenerations via a Tannakian interpretation for the functor of nearby cycles.

Keywords: Perverse sheaf, semiabelian variety, convolution product, generic vanishing theorem, Tannakian category

Krämer Thomas: Perverse sheaves on semiabelian varieties. Rend. Sem. Mat. Univ. Padova 132 (2014), 83-102. doi: 10.4171/RSMUP/132-7