At this point, we introduce the fibre functor suggested by Deligne. The proof that it is in fact a fibre functor is given in the Appendix.
Theorem 3.1. (Deligne) Denoting by
j0 : Gm/k ⊂ A1/k
the inclusion, the construction
M H0(A1/k, j0!M)
is a fibre functor on the Tannakian category P.
For any Kummer sheaf Lχ on Gm/k, the operation M M ⊗ Lχ is an autoequivalence of P with itself as Tannakian category. So we get the following corollary.
Corollary 3.2. For any Kummer sheaf Lχ on Gm/k, the construction
M H0(A1/k, j0!(