PGLn AND AUTOMORPHISMS OF PROJECTIVE SPACE
نویسنده
چکیده
where we view Gm(S) as the subgroup of invertible scalars in GLn(S). Define PGLn = s ◦ P̃GLn to be its sheafification (taken in the sense of Problem 8 on PS 2). Our goal will be to show that PGLn is an affine group scheme that represents automorphisms of projective space in the sense that PGLn(S) ' AutS(S × Pn−1). Before we begin, we require some preliminaries about Zariski sheaves. Let F : Sch→ Grp be a presheaf, and recall that all limits and colimits exist in Grp. Then, we say that F is stalky if, for any affine Spec(A) and any p ∈ Spec(A), the natural map
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