On the Rigidity of BN-sheaves

We define monoidal components attached to perverse sheaves on abelian varieties and discuss their properties

Multiplicity one for certain paramodular forms of genus two

We show that certain paramodular cuspidal automorphic irreducible representations of $\mathrm{GSp}(4,\mathbb{A}_\mathbb{Q})$, which are not CAP, are globally generic. This implies a multiplicity one theorem for paramodular cuspidal automorphic representations. Our proof relies on a reasonable hypothesis concerning the non-vanishing of central values of automorphic $L$-series.Comment: 10 page