About
Calculator
Ordering
FAQ
Download
Download Magma
Databases
User Contributions
Documentation
Handbook
Overview
Release Notes
Discovering Maths with Magma
First Steps in Magma (pdf)
Solving Problems with Magma (pdf)
Acknowledgements
Citations
Conferences
Links
Contact
CAG
Login
Magma
Computer • algebra
Documentation
Up
Contents
Index
Search
Expand all
Collapse all
Introduction
Motivation
Definitions
Classification of varphi-modules
Connection with Galois Representations
varphi-modules and Galois Representations in Magma
varphi-modules
Category
Creation Functions
PhiModule(M) : AlgMatElt -> PhiMod
ElementaryPhiModule(S,d,h) : RngSerLaur, RngIntElt, RngIntElt -> PhiMod
PhiModuleElement(x,D) : AlgMatElt, PhiMod -> PhiModElt
Attributes of varphi-modules
Dimension(D) : PhiMod -> RngIntElt
CoefficientRing(D) : PhiMod -> RngSerLaur
FrobeniusMatrix(D) : PhiMod -> AlgMatElt
Basic Operations and Properties of varphi-modules
IsEtale(D) : PhiMod -> BoolElt
ChangePrecision(~D, prec) : PhiMod, RngIntElt ->
DirectSum(D1, D2) : PhiMod, PhiMod -> PhiMod
BaseChange(~D, P) : ~PhiMod, AlgMatElt ->
RandomBaseChange(~D) : PhiMod ->
Phi(D, x) : PhiMod, PhiModElt -> PhiModElt
Reduction of varphi-modules and Galois Representations
SemisimpleDecomposition(D) : PhiMod -> AlgMatElt, AlgMatElt, SeqEnum, SeqEnum
Slopes(D) : PhiMod -> SeqEnum
SSGaloisRepresentation(D) : PhiMod -> SSGalRep
Semisimple Galois Representations
Category
Creation Functions
SSGaloisRepresentation(E,K,w,P) : FldFin, RngSerLaur, SeqEnum, SeqEnum -> SSGalRep
Basic Operations
CoefficientRing(V) : SSGalRep -> FldFin
FixedField(V) : SSGalRep -> RngSerLaur
Weights(V) : SSGalRep -> SeqEnum
Representation Associated to a varphi-Module
SSGaloisRepresentation(D) : PhiMod -> SSGalRep
Examples
Example
pAdicGalois_generic (H100E1)
Up
Contents
Index
Search
V2.28, 28 February 2025