Riemann-Roch, Stability and New Non-Abelian Zeta Functions for Number Fields
نویسنده
چکیده
Let F be a number field with discriminant ∆F . Denote its (normalized) absolute values by SF , and write SF = Sfin · ∪ S∞, where S∞ denotes the collection of all archimedean valuations. For simplicity, we use v (resp. σ) to denote elements in Sfin (resp. S∞). Denote by A = AF the ring of adeles of F , by Glr(A) the rank r general linear group over A, and write A := Afin ⊕A∞ and GLr(A) := GLr(A)fin × GLr(A)∞ according to their finite and infinite parts. For any g = (g fin : g∞) = (gv; gσ) ∈ GLr(A), define the injective morphism i(g) := i(g∞) : F r → A by (f) 7→ (f ; gσ · f). Let F (g) := Im ( i(g) ) and set
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