Galois module structure of the units modulo \(p^m\) of cyclic extensions of degree \(p^n\)
From MaRDI portal
Publication:2700861
DOI10.1007/s00229-022-01385-zOpenAlexW3164821344MaRDI QIDQ2700861
Andrew Schultz, John R. Swallow, Mináč, Ján
Publication date: 27 April 2023
Published in: Manuscripta Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2105.13216
Separable extensions, Galois theory (12F10) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Construction of unipotent Galois extensions and Massey products
- Parameterizing solutions to any Galois embedding problem over \(\mathbb{Z}/p^n\mathbb{Z}\) with elementary \(p\)-abelian kernel
- Triple Massey products and Galois theory
- Massey products \(\langle y,x,x,\ldots ,x,x,y\rangle\) in Galois cohomology via rational points
- Counting Galois \(\mathbb{U}_4(\mathbb{F}_p)\)-extensions using Massey products
- Quotients of absolute Galois groups which determine the entire Galois cohomology
- Pro-\(p\) groups with constant generating number on open subgroups.
- Galois cohomology of a number field is Koszul
- Galois module structure of Milnor \(K\)-theory in characteristic \(p\)
- Galois module structure of Milnor \(K\)-theory mod \(p^s\) in characteristic \(p\)
- Reconstruction of function fields
- Patching over fields
- Automatic realization of Galois groups with cyclic quotient of order \(p^n\)
- Applications of patching to quadratic forms and central simple algebras
- Representations of finite groups in characteristic \(p^r\).
- Coverings of the affine line in characteristic \(p>0\) and Abhyankar's conjecture
- Abhyankar's conjecture on Galois groups over curves
- Galois module structure of \(p\)th-power classes of extensions of degree \(p\)
- The Galois action and cohomology of a relative homology group of Fermat curves
- Triple Massey products and absolute Galois groups
- Galois embedding problems with cyclic quotient of order \(p\)
- Witt rings and Galois groups
- Enhanced Koszul properties in Galois cohomology
- Koszul algebras and quadratic duals in Galois cohomology
- Splitting varieties for triple Massey products
- Noether's problem and descent
- Homomorphisms of multiplicative groups of fields preserving algebraic dependence
- Galois \(p\)-groups and Galois modules
- Galois action on the homology of Fermat curves
- Torsion points on Fermat Jacobians, roots of circular units and relative singular homology.
- 2-nilpotent real section conjecture
- On the multiplicative group of cyclic \(p\)-extensions of a local field
- Index-stable compact \(p\)-adic analytic groups
- On the indecomposability of a remarkable new family of modules appearing in Galois theory
- Introduction to birational anabelian geometry
- n-Nilpotent Obstructions to pi_1 Sections of P^1-{0,1,infty} and Massey Products
- Triple Massey products vanish over all fields
- On the descending central sequence of absolute Galois groups
- Four-fold Massey products in Galois cohomology
- Algebraic Patching
- GALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF CYCLIC EXTENSIONS OF DEGREE pn
- Local-global principles for torsors over arithmetic curves
- Field Arithmetic
- Galois module structure of Galois cohomology for embeddable cyclic extensions of degree p n
- Milnor K_2 and field homomorphisms
- The Normal Closures of Certain Kummer Extensions
- A Gentle Course in Local Class Field Theory
- On Cyclic Fields
- Euklidische Körper und euklidische Hüllen von Körpern.
- Reconstruction of higher-dimensional function fields
- Local-global principles for tori over arithmetic curves
- Abhyankar’s conjectures in Galois theory: Current status and future directions
- Virtual retraction and Howson’s theorem in pro-$p$ groups
- Relations in the maximal pro-𝑝 quotients of absolute Galois groups
- On 3-Nilpotent Obstructions to π1 Sections for $$ \mathbb{P}^{1}_\mathbb{Q}$$−{0,1, $$\infty$$}
- Galois Theory and Projective Geometry
- Universal Spaces for Unramified Galois Cohomology
- Subgroup properties of Demushkin groups
- $p$-groups have unbounded realization multiplicity
- Galois module structure of Galois cohomology and partial Euler-Poincaré characteristics
- Detecting pro-p-groups that are not absolute Galois groups
- Classification of Demushkin Groups
- The Integral Representation Ring a(R k G)
- Representations of the cyclic groups of prime order 𝑝 over residue classes 𝑚𝑜𝑑𝑝^{𝑠}
- Determination of a Certain Family of Finite Metabelian Groups
This page was built for publication: Galois module structure of the units modulo \(p^m\) of cyclic extensions of degree \(p^n\)