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## Book.AlgebraicGeometry istorija

2017 rugsėjo 22 d., 11:55 atliko AndriusKulikauskas -
Pakeistos 1-6 eilutės iš
See: [[Geometry]]

Ravi Vakil: The intuition for schemes can be built on the intuition for affine complex varieties. Allen Knutson and Terry Tao have pointed out that this involves three different simultaneous generalizations, which can be interpreted as three large themes in mathematics.
* (i) We allow nilpotents in the ring of functions, which is basically analysis (looking at near-solutions of equations instead of exact solutions).
* (ii) We glue these affine schemes together, which is what we do in differential geometry (looking at manifolds instead of coordinate patches).
* (iii) Instead of working over C (or another algebraically closed field), we work more generally over a ring that isn’t an algebraically closed field, or even a field at all, which is basically number theory (solving equations over number fields, rings of integers, etc.).
į:
See: [[Geometry]]
2017 rugpjūčio 09 d., 09:40 atliko AndriusKulikauskas -
Pridėtos 1-2 eilutės:
See: [[Geometry]]
2017 rugpjūčio 09 d., 09:40 atliko AndriusKulikauskas -
Pakeistos 4-5 eilutės iš
* (iii) Instead of working over C (or another algebraically closed field), we work more generally over a ring that isn’t an algebraically closed field, or even a field at all, which is basically number
theory (solving equations over number fields, rings of integers, etc.).
į:
* (iii) Instead of working over C (or another algebraically closed field), we work more generally over a ring that isn’t an algebraically closed field, or even a field at all, which is basically number theory (solving equations over number fields, rings of integers, etc.).
2017 rugpjūčio 09 d., 09:40 atliko AndriusKulikauskas -
Pridėtos 1-5 eilutės:
Ravi Vakil: The intuition for schemes can be built on the intuition for affine complex varieties. Allen Knutson and Terry Tao have pointed out that this involves three different simultaneous generalizations, which can be interpreted as three large themes in mathematics.
* (i) We allow nilpotents in the ring of functions, which is basically analysis (looking at near-solutions of equations instead of exact solutions).
* (ii) We glue these affine schemes together, which is what we do in differential geometry (looking at manifolds instead of coordinate patches).
* (iii) Instead of working over C (or another algebraically closed field), we work more generally over a ring that isn’t an algebraically closed field, or even a field at all, which is basically number
theory (solving equations over number fields, rings of integers, etc.).

#### AlgebraicGeometry

Naujausi pakeitimai

 Puslapis paskutinį kartą pakeistas 2017 rugsėjo 22 d., 11:55