Every Voevodsky motive over a global field now has a canonical L-function that is multiplicative on exact triangles, with a functional equation in characteristic p.
A youb Les six opérations de Grothendieck et le formali sme des cycles évanescents dans le monde motivique, I, II, Astérisque 314–315, SMF
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Zeta and L functions of Voevodsky motives
Every Voevodsky motive over a global field now has a canonical L-function that is multiplicative on exact triangles, with a functional equation in characteristic p.