On the Gross-Keating invariant of a quadratic form over a non-archimedean local field

2015/04/28 by Tamotsu Ikeda, Ikeda, Tamotsu, Hidenori Katsurada +1
Computer Science · Engineering · Mathematics · #11E08 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1504.07330

openalex publication_date 2015/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let B be a half-integral symmetric matrix of size n defined over ℚ_p. The Gross-Keating invariant of B was defined by Gross and Keating, and has important applications to arithmetic geometry. But the nature of the Gross-Keating invariant was not understood very well for n≥ 4. In this paper, we establish basic properties of the Gross-Keating invariant of a half-integral symmetric matrix of general size over an arbitrary non-archimedean local field of characteristic zero.

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