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- Geometrically_regular_ring abstract "In algebraic geometry, a geometrically regular ring is a Noetherian ring over a field that remains a regular ring after any finite extension of the base field. Geometrically regular schemes are defined in a similar way. In older terminology, points with regular local rings were called simple points, and points with geometrically regular local rings were called absolutely simple points. Over fields that are of characteristic 0, or algebraically closed, or more generally perfect, geometrically regular rings are the same as regular rings. Geometric regularity originated when Chevalley and Weil pointed out to Zariski (1947) that, over non-perfect fields, the Jacobian criterion for a simple point of an algebraic variety is not equivalent to the condition that the local ring is regular.A Noetherian local ring containing a field k is geometrically regular over k if and only if it is formally smooth over k.".
- Geometrically_regular_ring wikiPageID "40023277".
- Geometrically_regular_ring wikiPageRevisionID "565666372".
- Geometrically_regular_ring subject Category:Algebraic_geometry.
- Geometrically_regular_ring subject Category:Commutative_algebra.
- Geometrically_regular_ring comment "In algebraic geometry, a geometrically regular ring is a Noetherian ring over a field that remains a regular ring after any finite extension of the base field. Geometrically regular schemes are defined in a similar way. In older terminology, points with regular local rings were called simple points, and points with geometrically regular local rings were called absolutely simple points.".
- Geometrically_regular_ring label "Geometrically regular ring".
- Geometrically_regular_ring sameAs m.0wdslrq.
- Geometrically_regular_ring sameAs Q17097939.
- Geometrically_regular_ring sameAs Q17097939.
- Geometrically_regular_ring wasDerivedFrom Geometrically_regular_ring?oldid=565666372.
- Geometrically_regular_ring isPrimaryTopicOf Geometrically_regular_ring.