Geometry of Schemes - NALG132
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This is an introductory lecture to the theory of schemes, a powerful tool which connected classical algebraic geometry to
number theory and made it possible to resolve several hard problems. The concepts in the lecture will be illustrated on
examples.
Last update: T_KA (20.05.2010)
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[1] D. Eisenbud, J. Harris: Geometry of Schemes, Springer-Verlag, New York, 2000. [2] R. Hartshorne: Algebraic Geometry, Springer-Verlag, New York-Heidelberg, 1977. Last update: T_KA (20.05.2010)
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1. Spectrum of a ring, affine schemes 2. Schemes in general 3. Morphisms of schemes, related constructions on schemes 4. Projective schemes, invariants
The contents of the lecture can be adjusted if there is demand to discuss more some topics from commutative algebra, or if there is an interest to look more in detail at examples. Last update: T_KA (20.05.2010)
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Some familiarity with basics of commutative algebra, properties of polynomial rings over a field and algebraic varieties. Last update: T_KA (20.05.2010)
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