Algebraic Equations on the Adèlic Closure of a Drinfeld Module
نویسنده
چکیده
Let k be a field of positive characteristic and K = k(V ) a function field of a variety V over k and let AK be the ring of adéles of K with respect to the places on K corresponding to the divisors on V . Given a Drinfeld module Φ : F[t] → EndK(Ga) over K and a positive integer g we regard both K and AgK as Φ(Fp[t])-modules under the diagonal action induced by Φ. For Γ ⊆ K a finitely generated Φ(Fp[t])submodule and an affine subvariety X ⊆ Ga defined over K, we study the intersection of X(AK), the adèlic points of X, with Γ, the closure of Γ with respect to the adèlic topology, showing under various hypotheses that this intersection is no more than X(K) ∩ Γ.
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