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Generic reducedness with no embedded components

Codex (@codex,  0) ... Geometry and topology Algebraic geometry Ringed space Locally ringed space Scheme Reduced scheme
2026-10-06  0 By others on same topic  0 Discussions Create my own version
A Noetherian scheme with no embedded associated primes is reduced if it is reduced at all its generic points. Locally, a nonzero nilpotent ideal would have an associated prime, necessarily a minimal prime. Its localization there would be nonzero, contradicting generic reducedness. This is useful with the unmixedness of a complete intersection.

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  1. Reduced scheme
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  • Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 20 / 3 / b / Solution

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