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Convolution and Equidistribution by Nicholas M. Katz

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CHAPTER 27

G2 Examples: Construction in Odd Characteristic

The situation in odd characteristic is complicated by the quadratic character χ2: the ! hypergeometric sheaf of type (7, 1)

F(χ2,k) := (A–7)degH(image, image, image2222; χ2),

though lisse on Gm, is not pure of weight zero, nor is its Ggeom the group G2. One knows [Ka-ESDE, 8.4.7] that this sheaf sits in a short exact sequence

0 VLχ2 → F(χ2,k) (A–7)degKl(, , 222)(1) 0,

with

V := ...

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