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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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