course-details-portlet

MA8203 - Algebraic Geometry

About

Examination arrangement

Examination arrangement: Oral examination
Grade: Passed/Failed

Evaluation form Weighting Duration Examination aids Grade deviation
Oral examination 100/100

Course content

The course introduces the central concepts of algebraic geometry. Affine and projective varieties are introduced, and these and their morphisms are studied.

The concept of a sheaf on a topological space is introduced, and in particular affine and projective varieties are interpreted as the locally ringed spaces. Sheaves of modules and the concept of sheafification are discussed.

Beyond these basic concepts the content of the course may vary, and include for instance divisors, resolutions of singularities, Riemann-Roch theorem for curves, elliptic curves, Bezout’s theorem, sheaf cohomology, schemes.

The course is taught every third year, next time Spring 2021. If there are few students, there will be guided self-study.

Learning outcome

1. Knowledge.
The student knows the basic concepts of algebraic geometry, in particular algebraic varieties with their structure sheaves, and the categories of coherent sheaves on these.
Further the student is familiar with some more advanced subjects, depending on the course content that year.

2. Skills.
The students should learn the topics mentioned above and be able to apply these concepts in own research.

Learning methods and activities

Lectures, some tasks for homework, alternatively as guided self-study.

Compulsory assignments

  • Exercises

Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

Required previous knowledge

Participants need some knowledge of (commutative) rings and modules, in particular the definitions of these. Moreover they should know the concept of localization of a commutative ring with respect to a multiplicative subset.

Course materials

Will be announced at the start of the course.

More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Doctoral degree level

Coursework

Term no.: 1
Teaching semester:  SPRING 2021

Language of instruction: -

Location: Trondheim

Subject area(s)
  • Algebra
Contact information
Course coordinator:

Department with academic responsibility
Department of Mathematical Sciences

Phone:

Examination

Examination arrangement: Oral examination

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam Room *
Autumn ORD Oral examination 100/100
Room Building Number of candidates
Spring ORD Oral examination 100/100
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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