Classification of varphi-modules
Connection with Galois Representations
varphi-modules and Galois Representations in Magma
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
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 (H93E1)
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012