手册

数学

Discovery

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Introduction E9F5FC

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software

Book.AlgebraicGeometry istorija

Paslėpti nežymius pakeitimus - Rodyti kodo pakeitimus

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
Tweet