Algebraic Geometry
《Algebraic Geometry》 · 第 241 页 · Chapter III，Section 7，Definition
Let $X$ be a proper scheme of dimension $n$ over $k$. A dualizing sheaf for $X$ is a coherent sheaf $\omega_X^\circ$, together with a trace map $t:H^n(X,\omega_X^\circ)\to k$, such that for all coherent sheaves $\mathcal F$ on $X$, the natural pairing induces an isomorphism $\operatorname{Hom}(\mathcal F,\omega_X^\circ)\cong H^n(X,\mathcal F)'$.