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Relative integral spinor norm groups over dyadic local fields

Constantin-Nicolae Beli

Abstract

We give explicit formulas for the relative integral spinor norm group $θ(X(M/N))$ in the case when the base field is a local dyadic field.

Relative integral spinor norm groups over dyadic local fields

Abstract

We give explicit formulas for the relative integral spinor norm group in the case when the base field is a local dyadic field.
Paper Structure (8 sections, 92 theorems, 43 equations)

This paper contains 8 sections, 92 theorems, 43 equations.

Table of Contents

  1. Introduction and background to BONG theory
  2. The maps $g$ and $G$ revisited
  3. Preliminary results
  4. The set of all not norm generators of a lattice
  5. BONGs of lattices with $\theta (O^+(L))\neq\dot{F}$
  6. Two reduction steps
  7. Main results
  8. Appendix

Key Result

Lemma 1.2

Let $a,c\in\dot{F}$ and let $\alpha\in{\mathbb R}\cup\{\infty\}$. (i) We have $(1+\mathfrak p^{\alpha})\dot{F}^2\subseteq{\rm N} (c)$ iff $\alpha +d(c)>2e$. (ii) We have $(1+\mathfrak p^{\alpha})\dot{F}^2\cap{\rm N} (a )\subseteq{\rm N} (c)$ iff $\alpha +\max\{ d(ac),d(c)\} >2e$.

Theorems & Definitions (96)

  • Lemma 1.2
  • Lemma 1.3
  • Lemma 1.4
  • Lemma 1.5
  • Proposition 1.6
  • Theorem 1.7
  • Theorem 1.9
  • Lemma 1.10
  • Lemma 1.11
  • Theorem 1.12
  • ...and 86 more