On the asymptotics of wildly ramified local function field extensions / by Raphael Müller ; Supervisor: Prof. Dr. Jürgen Klüners. Paderborn, 2023
Content
- Local Function Fields
- Introduction to Local Function Fields
- Valuation Theory
- Galois group and Galois closure
- Artin-Schreier Theory
- System of Representatives of J(F)
- Ramification Theory
- Abelian Conductor-Discriminant-Formula
- Asymptotics and Tauberian Theorems
- Cohomology and Explicit Construction
- Abelian Conductor Density
- Certain Quotient Groups of the Unit Group
- Conductor Density of Abelian p-groups
- Conductor Density of Arbitrary Finite Abelian Groups
- Lower Bounds on Discriminant Density
- On Subgroups of Affine Linear Groups AGL1(q)
- Affine Linear Groups and Semi-direct Products
- Decomposition of J(L) for a Tamely Ramified Extension L/F
- On Constructing Subgroups of Cp Cp
- Heisenberg Groups and Arithmetic of Cp-Extensions
- Galois Module Theory
- Description of (Twisted) Heisenberg Extensions
- Minimal Heisenberg Extensions
- Minimal Twisted Heisenberg Extensions
- Heisenberg Modules and Systems of Representatives
- Counting Heisenberg Extensions over p2 Points
- Counting Twisted Heisenberg Extensions over p2 Points
- On Galois Twisted Heisenberg Group Extensions
- Bibliography
- Notation Index