Construction of the Lindström valuation of an algebraic extension
arXiv:1704.08671 · doi:10.1016/j.jcta.2018.03.003
Abstract
Recently, Bollen, Draisma, and Pendavingh have introduced the Lindström valuation on the algebraic matroid of a field extension of characteristic p. Their construction passes through what they call a matroid flock and builds on some of the associated theory of matroid flocks which they develop. In this paper, we give a direct construction of the Lindström valuated matroid using the theory of inseparable field extensions. In particular, we give a description of the valuation, the valuated circuits, and the valuated cocircuits.
12 pages, v2: added Section 3 on valuated cocircuits and minors, v3: minor changes and corrections, final submitted version