Weil Conjectures (Deligne’s Purity Theorem)
نویسندگان
چکیده
Let κ = Fq be a finite field of characteristic p > 0, and k be a fixed algebraic closure of κ. We fix a prime ` 6= p, and an isomorphism τ : Q` → C. Whenever we want to denote something (e.g. scheme, sheaf, morphism, etc.) defined over κ, we will put a subscript 0 (e.g. X0 is a scheme over κ, F0 is a Weil sheaf defined over X0, etc.), and when the subscript is dropped, this means the corresponding base change to k (e.g. X = X0 ×κ k, F is the pullback of F0 via X → X0, etc.). For a closed point a ∈ |X0|, we’ll use the subscript Fa to denote the stalk of a sheaf F at a geometric (k)-point a over a. This will avoid any confusion, for example, about the stalks at 0 for a sheaf on A0.
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