In 2008, Boij and Söderberg, stated a couple of conjecture for
the extremal rays of Betti cone over the polynomial ring. They also
shown that these conjectures imply the Multiplicity conjecture. In 2009,
Eisenbud and Schreyer resolve Boij-Söderberg’s conjectures. In this
series, we discuss Boij-Söderberg theory for standard graded k-algebras.
We note the obstacles in using their techniques in the general situation
and identify classes of rings where we can prove some of these results.
