Commutative character sheaves and geometric types for supercuspidal representations

We show that some types for supercuspidal representations of tamely ramified p-adic groups appear in Jiu-Kang Yu’s work are geometrizable. To do so, we define a function-sheaf dictionary one-dimensional characters arbitrary smooth group schemes over finite fields. In previous considered the case commutative and found standard definition character sheaves produced with nontrivial kernel. this paper give modification category remedies defect, is also extensible to non-commutative groups. then use these geometrize linear introduced by Yu, assuming vanishes on certain derived subgroup. geometric types, combine Gurevich Hadani’s geometrization Weil representation Lusztig’s sheaves.