Algebraic matroids and Frobenius flocks

Bollen, Guus P.; Draisma, Jan; Pendavingh, Rudi (2018). Algebraic matroids and Frobenius flocks. Advances in mathematics, 323, pp. 688-719. Elsevier 10.1016/j.aim.2017.11.006

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We show that each algebraic representation of a matroid M in positive characteristic determines a matroid valuation of M , which we have named the {\em Lindström valuation}. If this valuation is trivial, then a linear representation of M in characteristic p can be derived from the algebraic representation. Thus, so-called rigid matroids, which only admit trivial valuations, are algebraic in positive characteristic p if and only if they are linear in characteristic p. To construct the Lindström valuation, we introduce new matroid representations called flocks, and show that each algebraic representation of a matroid induces flock representations.

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