I'd like to know when is it possible (and makes sense) to find a relation between the cotangent and the dualizing complex in the setting of algebraic geometry
2026-03-30 03:24:58.1774841098
Relation between dualizing complex and cotangent complex
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For varities that are local complete intersections (inside the projective space) , the cotangent complex is a perfect complex and hence there is a good notion of determinant. In this case it follows that determinant of the cotangent complex is the dualizing sheaf. This more or less follows by definition and Hartshorne Chapter 3, Theorem 7.11. I am not sure what happens outside this relatively easy case.