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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
153:
that is being extended may be considered the ground field for an argument or discussion. Within algebraic geometry, from the point of view of
177:-schemes, and its structure and symmetry may be richer than the fact that the space of the scheme is a point might suggest.
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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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50:It is used in various areas of algebra:
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223:"Abstract algebraic geometry"
247:"Form of an algebraic group"
252:Encyclopedia of Mathematics
228:Encyclopedia of Mathematics
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88:abstract algebraic variety
181:In Diophantine geometry
165:) of the ground field
126:algebraic varieties).
70:In algebraic geometry
195:algebraically closed
187:diophantine geometry
277:Field (mathematics)
199:field of definition
193:is not taken to be
173:in the category of
118:vector spaces) and
62:, the concept of a
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203:Galois cohomology
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18:Groundfield
271:Categories
138:, given a
80:André Weil
257:EMS Press
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259:, 2001
235:, 2001
197:. The
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209:Notes
90:over
37:field
35:is a
159:Spec
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185:In
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58:In
46:Use
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