Definition 49.9.1. Let $f : Y \to X$ be a flat locally quasi-finite morphism of locally Noetherian schemes. Let $\omega _{Y/X}$ be the relative dualizing module and let $\tau _{Y/X} \in \Gamma (Y, \omega _{Y/X})$ be the trace element (Remarks 49.2.11 and 49.4.7). The annihilator of

is the *different* of $Y/X$. It is a coherent ideal $\mathfrak {D}_ f \subset \mathcal{O}_ Y$.

## Comments (3)

Comment #7483 by Hao Peng on

Comment #7484 by Hao Peng on

Comment #7631 by Stacks Project on