Geometric Class Field Theory Ii
نویسنده
چکیده
Homcts(π1,ét(C),Q × ` ) ∼= Hom(Pic0(k),Q` ) + (Ẑ Frobc −−−→ Q` ). where c ∈ C(Fq) is a fixed rational point. Our proof will proceed by upgrading this equality to an equivalence of geometric objects. First, we’ll interpretHomcts(π1,ét(C),Q × ` ) in terms of rank one `-adic local systems on C. Similarly, we’ll interpret the datum of Hom(Pic0(k),Q` ) + (Ẑ Frobc −−−→ Q` ) as a “character sheaf” on PicC . In broader context, this is a rank one `-adic local system satisfyng a “Hecke eigensheaf” condition.
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