Linkage theory, also known as liaison theory, became a major topic after the work of Peskine and Szpiro. Since then, it has become an important tool in commutative algebra, especially in the study of perfect ideals and in constructing and comparing different classes of ideals.
In this talk, I will introduce complete intersection linkage and Gorenstein linkage, and discuss the glicci conjecture: whether every Cohen–Macaulay ideal in a regular ring lies in the Gorenstein linkage class of a complete intersection. I will then explain the techniques of Bourbaki sequences and doubly layered modules, which are used to prove that several classes of ideals are glicci, including m-primary ideals in Gorenstein rings, height-three monomial ideals, and monomial ideals with clean prime filtrations. These results provide new evidence for the conjecture and establish it in dimension three over regular rings.
