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of a variety given abstractly may be smaller than the ground field, and two varieties may become isomorphic when the ground field is enlarged, a major topic in
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that is being extended may be considered the ground field for an argument or discussion. Within algebraic geometry, from the point of view of
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the characteristic problems of the subject are those caused by the fact that the ground field
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Reference to a ground field may be common in the theory of
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212:"Abstract algebraic geometry"
236:"Form of an algebraic group"
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241:Encyclopedia of Mathematics
217:Encyclopedia of Mathematics
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77:abstract algebraic variety
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170:In Diophantine geometry
154:) of the ground field
115:algebraic varieties).
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59:In algebraic geometry
184:algebraically closed
176:diophantine geometry
266:Field (mathematics)
188:field of definition
182:is not taken to be
162:in the category of
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18:mathematics
260:Categories
127:, given a
69:André Weil
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248:, 2001
224:, 2001
186:. The
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198:Notes
79:over
26:field
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148:Spec
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