  The question of the existence of a polynomial kernelization of the Vertex
Cover Above LP problem has been a longstanding, notorious open problem in
Parameterized Complexity. Five years ago, the breakthrough work by Kratsch and
Wahlstrom on representative sets has finally answered this question in the
affirmative [FOCS 2012]. In this paper, we present an alternative, algebraic
compression of the Vertex Cover Above LP problem into the Rank Vertex Cover
problem. Here, the input consists of a graph G, a parameter k, and a bijection
between V (G) and the set of columns of a representation of a matriod M, and
the objective is to find a vertex cover whose rank is upper bounded by k.
