The excluded minors for the class of matroids that are binary or ternary

We show that the excluded minors for the class of matroids that are binary or ternary are U2,5U2,5, U3,5U3,5, U2,4⊕F7U2,4⊕F7, U2,4⊕F7∗, U2,4⊕2F7U2,4⊕2F7, U2,4⊕2F7∗, and the unique matroids obtained by relaxing a circuit-hyperplane in either AG(3,2) or T12T12. The proof makes essential use of results obtained by Truemper on the structure of almost-regular matroids.