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Residual Finiteness of Commutative Rings and Schemes

  • Aron Simis (a1)

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This work grew out of a preliminary announcement (Notices of the Amer. Math. Soc. 18 (1971)). Here we modify the definition of residual finiteness given in [2]. This allows us, first of all, to consider a broader class of rings which are “essentially” residually finite and, secondly, to extend the notion to schemes. We then show that, for various topologies on the category of schemes, our notion of residual finiteness is local so that all relevant questions appear already at the ring level.

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References

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1. Bourbaki, N., Algèbre commutative (Hermann, Paris, 1961, 1965).
2. Chew, K. L., and Lawn, S., Residually finite rings, Can. J. Math. 22 (1970), 92101.
3. Grothendieck, A., Éléments de géométrie algébrique, Publications Mathématiques (IHES).
4. Lazard, D., Les épimorphismes d'anneaux, Séminaire d'Algèbre Commutative Samuel, P., Exposé 4 (Paris, 1968).
5. Matsumura, H., Commutative algebra (Benjamin, W. A., Inc., New York, 1970).
6. Raynaud, M., Anneaux locaux henséliens, Lecture Notes in Mathematics, Springer-Verlag no. 169 (1970).
7. Roby, N., Les épimorphismes d'anneaux, Séminaire d'Algèbre Commutative Samuel, P. Exposé 8 (Paris, 1968).
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Residual Finiteness of Commutative Rings and Schemes

  • Aron Simis (a1)

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