The current status of the conjecture on algebraic matroids Can anyone point out some articles for the conjecture: the dual of an algebraic matroid is algebraic?
Thank you!
 A: I believe this is still open. In Matroid Theory Second Edition by Oxley which was published in 2011 this is listed as an open problem. This problem is addressed twice in the book. First on page 219 Oxley writes: "Probably most basic unsolved problem in the study of algebraic matroids is the following..." He then lists exactly this question on the dual of an algebraic matroid. It then says Lindstrom (1985) shows that the question of whether the dual of an algebraic matroid is algebraic can be reduced to the following question:

If a matroid is algebraic over a field of a certain characteristic, then is its dual also algebraic over a field of this characteristic?

Later on page 585 Oxley says that the intractability of the problem in the original post "prompted Lindstrom (1988) to proposed the following question."

If a matroid is algebraic over a field of a certain characteristic, is its dual also algebraic over a field of the same characteristic?

These portions of the book appear to be unchanged from the First Edition published in 1992. So, it seems no major progress has been made. I'll list two papers of Lindstrom referenced below.
Lindstrom (1985): On algebraic representations of dual matroids. Department of Math., Univ. of Stockholm, Reports, No. 5.
Lindstrom (1988): Matroids, algebraic and non-algebraic. In Algebraic, extremal and metric combinatorics 1986.
I cannot find Lindstrom (1985), but Lindstrom (1988) can be found on MathSciNet.
