Author ORCID Identifier
Date Available
5-10-2024
Year of Publication
2024
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
Dr. David Leep
Abstract
Given two quadratic forms $Q_1, Q_2$ over a $p$-adic field $K$ in $n$ variables, we consider the pencil $\mathcal{P}_K(Q_1, Q_2)$, which contains all nontrivial $K$-linear combinations of $Q_1$ and $Q_2$. We define $D$ to be the maximal dimension of a subspace in $K^n$ on which $Q_1$ and $Q_2$ both vanish. We define $H$ to be the maximal number of hyperbolic planes that a form in $\mathcal{P}_K(Q_1, Q_2)$ splits off over $K$. We will determine which values for $(D, H)$ are possible for a nonsingular pair of quadratic forms over a $p$-adic field $K$.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2024.128
Recommended Citation
Hall, John, "Pairs of Quadratic Forms over p-Adic Fields" (2024). Theses and Dissertations--Mathematics. 111.
https://uknowledge.uky.edu/math_etds/111
