SPINOR GENERA UNDER Zp-EXTENSIONS
نویسندگان
چکیده
Let L be a quadratic lattice over a number field F . We lift the lattice L along a Zp-extension of F and investigate the growth of the number of spinor genera in the genus of L. Let Ln be the lattice obtained from L by extending scalars to the n-th layer of the Zp-extension. We show that, under various conditions on L and F , the number of spinor genera in the genus of Ln is 2 +O(1) where η is some rational number depending on L and the Zp-extension. The work involves Iwasawa’s theory of Zp-extensions and explicit calculation of spinor norm groups of local integral rotations.
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