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fixes (hopefully) #3841 #3866

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Jun 18, 2024
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fixes (hopefully) #3841 #3866

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22 changes: 17 additions & 5 deletions experimental/GModule/src/GaloisCohomology.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -196,6 +196,7 @@
M = abelian_group([0 for x = o])
h = MapFromFunc(c.C.M, M, x->M([valuation(x.data, y) for y = o]))
D = gmodule(G, [hom(M, M, [h(action(c.C, g, c.C.M(i//1))) for i = o]) for g = gens(c.C.G)])
# @assert all(is_bijective, D.ac)

cc = map_entries(h, c, parent = D)
h2, mh2, icb = Oscar.GrpCoh.H_two(D)
Expand All @@ -204,7 +205,6 @@
if i == 2
return false, nothing
else
@show :trying_harder
continue
end
end
Expand Down Expand Up @@ -234,7 +234,7 @@
return true, res
end

function Oscar.map_entries(MI:: Oscar.GrpCoh.MultGrp{AbsSimpleNumFieldOrderFractionalIdeal}, c::Oscar.GrpCoh.CoChain{2, <:GAPGroupElem, Oscar.GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}})
function Oscar.map_entries(MI::Oscar.GrpCoh.MultGrp{AbsSimpleNumFieldOrderFractionalIdeal}, c::Oscar.GrpCoh.CoChain{2, <:GAPGroupElem, Oscar.GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}})
k = c.C.M.data
zk = maximal_order(k)
D = gmodule(c.C.G, [MapFromFunc(MI, MI, x->MI(hom(k, k, action(c.C, g, c.C.M(gen(k))).data)(x.data))) for g = gens(c.C.G)])
Expand Down Expand Up @@ -428,7 +428,7 @@

#if K/k is unramified, then the units are cohomological trivial,
# so Z (with trivial action) is correct for the gmodule
#if K/k is tame, then the 1-units are cohomologycal trivial, hence
#if K/k is tame, then the 1-units are cohomological trivial, hence
# Z time k^* is enough...

e = divexact(absolute_ramification_index(K), absolute_ramification_index(k))
Expand Down Expand Up @@ -513,7 +513,18 @@


@vprint :GaloisCohomology 2 " .. quotient ..\n"
Q, mQ = quo(U, [preimage(mU, 1+prime(k)^4*x) for x = o])
if prime(k) == 2
#we need val(p^k) > 1/(p-1)
#val(p) = 1 and the only critical one is p=2, where k>1 is
#neccessary
ex = 2
else
ex = 1

Check warning on line 522 in experimental/GModule/src/GaloisCohomology.jl

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Added line #L522 was not covered by tests
end
#x -> 1+pi*x is in general, not injective, not even for a basis
# if valuation(dm) == 0, then by Lorenz Alg II, 26.F10 it should
# be, but we're not using it. This was used to avoid exp
Q, mQ = quo(U, [preimage(mU, exp(prime(k)^ex*x)) for x = o])
S, mS = snf(Q)
Q = S
mQ = mQ*inv(mS)
Expand All @@ -525,7 +536,7 @@
end

@vprint :GaloisCohomology 2 " .. the module ..\n"
hh = [hom(Q, Q, [mQ(preimage(mU, mG(i)(mU(preimage(mQ, g))))) for g = gens(Q)]) for i=gens(G)]
hh = [hom(Q, Q, [mQ(preimage(mU, mG(i)(mU(preimage(mQ, g))))) for g = gens(Q)]; check = false) for i=gens(G)]
Hecke.assure_has_hnf(Q)
return gmodule(G, hh), mG, pseudo_inv(mQ)*mU
end
Expand Down Expand Up @@ -1287,6 +1298,7 @@
end

function local_index(CC::Vector{GrpCoh.CoChain{2, PermGroupElem, GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}}}, P::AbsSimpleNumFieldOrderIdeal, mG::Map = automorphism_group(PermGroup, Hecke.nf(order(P)))[2]; B::Any = nothing, index_only::Bool = false)

k = Hecke.nf(order(P))

if B !== nothing && haskey(B.lp, P)
Expand Down
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