Last week we defined a system of higher homotopies for a free resolution F. of a finitely generated module M over Q where fM = 0 and showed that they exist. When Q is a noetherian local ring and f is a non-zero divisor, we will see a proof of the Shamash construction which uses the system of higher homotopies to construct a resolution of M over R = Q/(f). Time permitting, we will observe some consequences and state some generalisations.
