Universität Regensburg   IMPRESSUM    DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
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Algebraic Geometry I
Semester
WiSe 2026 / 27

Lecturer
Guido Kings

Type of course (Veranstaltungsart)
Vorlesung

German title
Algebraische Geometrie I

Contents
Algebraic Geometry studies solutions of polynomial equations with geometric methods. This is
indispensable for many questions in Geometry and in the study of Diophantine Equations. More
precisely we will study sheaves, representable functors, schemes, group schemes and their basic
properties having in mind the arithmetic of one-dimensional schemes in particular elliptic curves.
This will lead eventually to a proof of the famous Riemann Roch Theorem and of the Weil conjectures
for elliptic curves.

Literature
will be announced during the course. There will be a script!

Recommended previous knowledge
Basic commutative algebra: modules, tensor product and localisation of modules.

Time/Date
Tuesday, Thursday 14-16. Exercises: Tuesday 10-12 M101

Location
Tuesday M101, Thursday M103

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=76283
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes: At least 50% of the exercises
Examination (Prüfungsleistungen)
  • Written exam: Duration: 120 Minutes, Date: TBA, re-exam: Date: TBA
Modules
BV, MV, MArGeo

ECTS
9
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