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  • Clifton Cunningham (a1) and David Roe (a2)

We consider the rigid monoidal category of character sheaves on a smooth commutative group scheme $G$ over a finite field $k$ , and expand the scope of the function-sheaf dictionary from connected commutative algebraic groups to this setting. We find the group of isomorphism classes of character sheaves on $G$ , and show that it is an extension of the group of characters of $G(k)$ by a cohomology group determined by the component group scheme of $G$ . We also classify all morphisms in the category character sheaves on $G$ . As an application, we study character sheaves on Greenberg transforms of locally finite type Néron models of algebraic tori over local fields. This provides a geometrization of quasicharacters of $p$ -adic tori.

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Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
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