A generalized Jacobian criterion for regularity
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- by Peter Seibt PDF
- Proc. Amer. Math. Soc. 93 (1985), 201-202 Request permission
Abstract:
For a commutative noetherian algebra $B$ over a perfect field $A$ regularity is equivalent to the flatness of ${\Omega _{B|A}}$ plus ${H_1}(A,B,B) = 0$ (simplicial homology). In characteristic 0 the homological condition is superfluous.References
- Michel André, Homologie des algèbres commutatives, Die Grundlehren der mathematischen Wissenschaften, Band 206, Springer-Verlag, Berlin-New York, 1974 (French). MR 0352220
- Michael Barr, A cohomology theory for commutative algebras. I, II, Proc. Amer. Math. Soc. 16 (1965), 1379–1384. MR 193119, DOI 10.1090/S0002-9939-1965-0193119-3
- Luc Illusie, Complexe cotangent et déformations. I, Lecture Notes in Mathematics, Vol. 239, Springer-Verlag, Berlin-New York, 1971 (French). MR 0491680
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 201-202
- MSC: Primary 13D03; Secondary 13H05
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770518-2
- MathSciNet review: 770518