Algebraic Number Theory

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Algebraic Number Theory

Semester
WiSe 2025 / 26

Lecturer
Niko Naumann

Type of course (Veranstaltungsart)
Vorlesung

German title
Algebraische Zahlentheorie

Contents
This course gives an introduction to Algebraic Number Theory. Together with the course on
Algebraic Geometry this course can serve as a basis for further specialization in the area of
Arithmetic Geometry. We treat number fields, rings of algebraic integers, Dedekind domains,
Minkowski's lattice point theory, finiteness of class numbers, Dirichlet's unit theorem,
ramification theory, local fields, valuations, and the product formula.

Literature
Froehlich, Taylor, Algebraic Number Theory, Cambridge University Press Lang, Algebraic Number
Theory, Springer. Neukirch, Algebraic Number Theory, Springer. Neukirch, Algebraische
Zahlentheorie, Springer

Recommended previous knowledge
Algebra and some commutative algebra (the latter can be reviewed, as needed)

Time/Date
Mon, 10 -- 12 and Fri, 12 --- 2 pm.

Location
H31

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=71696
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Registration for the exercise classes: In class.
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes: Successful participation in the
exercise classes: Active participation and the presentation of solutions to exercises at the
blackboard: Each participant has to present at least two solutions, at least one from the
exercise sheets 1-6 and at least one from the exercise sheets 7-12. Furthermore 50 %
successful written solutions to the exercises have to be submitted.

Examination (Prüfungsleistungen)

Written exam: Duration: 180 minutes, Date: TBD, re-exam: Date: TBD

Modules
BV, MV, MArGeo, LA-GyAlg

ECTS
9