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Additional
scheme theory
English Wikipedia - The Free Encyclopedia
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Scheme (mathematics)
In
mathematics
,
schemes
connect the fields of
algebraic geometry
,
commutative algebra
and
number theory
. Schemes were introduced by
Alexander Grothendieck
in 1960 in his treatise
Éléments de géométrie algébrique
, with the aim of developing the formalism needed to solve deep problems of algebraic geometry, such as the
Weil conjectures
(the last of which was proved by
Pierre Deligne
). Schemes enlarge the notion of
algebraic variety
to include
nilpotent
elements (the equations
x
= 0 and
x
2
= 0 define the same points, but different schemes), and "varieties" defined over any
commutative ring
.
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