Universität Wien
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250043 VO Schemes - Algebraic Geometry II (2022W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
ON-SITE

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

The course has 3 weekly hours (and 5 ECTS). These will be blocked in twice two hours weekly, because in some weeks there will be no classes due to absence.

  • Monday 03.10. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 04.10. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 10.10. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 11.10. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 17.10. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 18.10. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 24.10. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.10. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 31.10. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.11. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 08.11. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 14.11. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 15.11. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 21.11. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 22.11. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 28.11. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 29.11. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 05.12. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 06.12. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 12.12. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 13.12. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 09.01. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.01. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 16.01. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.01. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 23.01. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.01. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 30.01. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.01. 13:15 - 14:45 Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

This course will provide a rather concrete and direct approach to Grothendieck's theory of schemes, thus generalizing the classical concept of algebraic varieties. We will do algebraic geometry from a very conceptual point of view, associating to an arbitrary (commutative) ring a geometric object, its spectrum. With this construction, geometry is studied via commutative algebra.

Whereas standard texts like Hartshorne's book rely heavily on the theory of sheaves (Garben), we prefer to work directly with rings and their prime ideals. This simplifies enormously the approach.

A main point of the course will be to show the amazing elegance of Grothendieck's proposal. And this can be done in a rather accessible (and almost elementary) way.

We do not require much prior knowledge aside basic algebra (rings, ideals, homomorphisms, ...) nor do we rely on the former course "Introduction to Algebraic Geometry" from last spring term. So also newcomers will be able to follow and are very welcome.

Assessment and permitted materials

Oral exam at the end of the course by appointment.

Minimum requirements and assessment criteria

Examination topics

Reading list

Association in the course directory

MALV, MGEV

Last modified: Sa 07.09.2024 00:15