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• W1997325577 abstract "The celebrated Smith–Minkowski–Siegel mass formula expresses the mass of a quadratic lattice $(L,Q)$ as a product of local factors, called the local densities of $(L,Q)$ . This mass formula is an essential tool for the classification of integral quadratic lattices. In this paper, we will describe the local density formula explicitly by observing the existence of a smooth affine group scheme $underline{G}$ over $mathbb{Z}_{2}$ with generic fiber $text{Aut}_{mathbb{Q}_{2}}(L,Q)$ , which satisfies $underline{G}(mathbb{Z}_{2})=text{Aut}_{mathbb{Z}_{2}}(L,Q)$ . Our method works for any unramified finite extension of $mathbb{Q}_{2}$ . Therefore, we give a long awaited proof for the local density formula of Conway and Sloane and discover its generalization to unramified finite extensions of $mathbb{Q}_{2}$ . As an example, we give the mass formula for the integral quadratic form $Q_{n}(x_{1},dots ,x_{n})=x_{1}^{2}+cdots +x_{n}^{2}$ associated to a number field $k$ which is totally real and such that the ideal $(2)$ is unramified over $k$ ." @default.
• W1997325577 created "2016-06-24" @default.
• W1997325577 creator A5071306883 @default.
• W1997325577 date "2014-12-05" @default.
• W1997325577 modified "2023-10-18" @default.
• W1997325577 title "Group schemes and local densities of quadratic lattices in residue characteristic 2" @default.
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• W1997325577 doi "https://doi.org/10.1112/s0010437x14007829" @default.
• W1997325577 hasPublicationYear "2014" @default.
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