Smooth Compactifications of Certain Normic Bundles
نویسندگان
چکیده
For a finite cyclic Galois extension of fields K/k of degree n and a separable polynomial of degree dn or dn−1, we construct an explicit smooth compactification X → Pk of the affine normic bundle X0 given by NK/k(~z) = P (x) 6= 0, extending the map X0 → Ak, where (~z, x) 7→ x. The construction makes no assumption of the characteristic of k, making it a suitable departure point for studying the arithmetic of smooth compactifications of X0 over global fields of positive characteristic.
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تاریخ انتشار 2014