Construction of the Lindstr\"om valuation of an algebraic extension

Abstract

Recently, Bollen, Draisma, and Pendavingh have introduced the Lindstr\"om 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 Lindstr\"om 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.