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Fakultät für Mathematik Universität Regensburg
Arakelov Geometry
Semester
WiSe 2021 / 22

Lecturer
Walter Gubler

Type of course (Veranstaltungsart)
Vorlesung

German title
Arakelov Geometrie

Contents
Arakelov Geometry is a part of arithmetic geometry, where methods of algebra, geometry and
analysis are combined. Arakelov theory was popularized through Faltings's proof of the Mordell
conjecture. In this course, we will give the arithmetic intersection theory of Gillet-Soule on
arithmetic varieties which found many applications as Faltings's proof of the Mordell--Lang
conjecture for subvarieties of abelian varieties and as Ullmo's and Zhang's proof of the Bogomolov
conjecture.

Literature
Moriwaki: Arakelov Geometry Soule, Abramovich, Burnol, Kramer: Lectures on Arakelov Geometry

Recommended previous knowledge
Algebra, Commutative Algebra. It is recommended to take simultaneously Algebraic Geometry

Time/Date
Tuesaday, Thursday 8-10

Location
M104

Registration
  • Preliminary registration for the organisation of exercise classes: at the end of the previous
    semester via EXA or LSF (see announcement by the department)
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes: 50% of the points in the exercises
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 25 minutes, Date: tba, re-exam: Date: tba
Modules
BV, MV, MArGeo

ECTS
9