diff --git a/experimental/InjectiveResolutions/src/InjectiveResolutions.jl b/experimental/InjectiveResolutions/src/InjectiveResolutions.jl
index 8701b3d7f608..ab2c0e43f16c 100644
--- a/experimental/InjectiveResolutions/src/InjectiveResolutions.jl
+++ b/experimental/InjectiveResolutions/src/InjectiveResolutions.jl
@@ -713,9 +713,9 @@ function _get_irreducible_ideal(kQ::MonoidAlgebra, J::IndecInj)
 end
 
 @doc raw"""
-    irreducible_resolution(M::SubquoModule{<:MonoidAlgebraElem}, i::Int = 0)
+    irreducible_resolution(M::SubquoModule{<:MonoidAlgebraElem}, i::Int = -1)
 
-Return an irreducible resolution of $M$.
+Return an irreducible resolution of $M$ (up to cohomological degree i).
 
 !!! note
     The monoid algebra $k[Q]$ must be normal. 
@@ -759,7 +759,7 @@ by graded submodule of kQ^1 with 3 generators
 over monoid algebra over rational field with cone of dimension 2
 ```
 """
-function irreducible_resolution(M::SubquoModule{<:MonoidAlgebraElem}, i::Int=0)
+function irreducible_resolution(M::SubquoModule{<:MonoidAlgebraElem}, i::Int=-1)
   kQ = base_ring(M)
   @req is_normal(kQ) "monoid algebra must be normal"
 
@@ -812,7 +812,7 @@ function irreducible_resolution(M::SubquoModule{<:MonoidAlgebraElem}, i::Int=0)
     push!(cochain_maps, hi)
 
     # end at cohomological degree i
-    if i > 0 && j == i
+    if j == i + 1
       break
     end
     j = j + 1
@@ -955,7 +955,7 @@ function injective_resolution(M::SubquoModule{<:MonoidAlgebraElem}, i::Int)
   #compute irreducible resolution of shifted module
   a_shift = compute_shift(M, i+1)
   M_a = twist(M, -G(a_shift))
-  irr_res = irreducible_resolution(M_a)
+  irr_res = irreducible_resolution(M_a,i)
 
   #get injective modules up to cohomological degree i, i.e. J^0, J^1, ...,J^i
   inj_modules = Vector{InjMod}()
@@ -968,7 +968,7 @@ function injective_resolution(M::SubquoModule{<:MonoidAlgebraElem}, i::Int)
 
   #get all needed maps (as k-matrix or k[Q]-matrix?)
   cochain_maps = [
-    matrix(irr_res.cochain_maps[k]) for k in eachindex(irr_res.cochain_maps) if 1 < k <= i+1
+    matrix(irr_res.cochain_maps[k]) for k in eachindex(irr_res.cochain_maps) if 1 <= k <= i+1
   ]
   return InjRes(M, inj_modules, cochain_maps, length(inj_modules)-1, irr_res, a_shift)
 end
@@ -1065,4 +1065,3 @@ export zeroth_local_cohomology
 export MonoidAlgebra
 export MonoidAlgebraIdeal
 export MonoidAlgebraElem
-
diff --git a/experimental/InjectiveResolutions/src/LocalCohomology.jl b/experimental/InjectiveResolutions/src/LocalCohomology.jl
index 630d9377f3f7..5a9c5f9519ad 100644
--- a/experimental/InjectiveResolutions/src/LocalCohomology.jl
+++ b/experimental/InjectiveResolutions/src/LocalCohomology.jl
@@ -146,7 +146,7 @@ function local_cohomology(M::SubquoModule{T}, I::MonoidAlgebraIdeal, i::Integer)
 
   #get the injective modules J^{i-1} -> J^i -> J^{i+1}
   Ji_ = inj_res.inj_mods[i]
-  Ji = inj_res.inj_mods[i + 1]
+  Ji = inj_res.inj_mods[i+1]
 
   if inj_res.upto > i # J^{i+1} ≠ 0
     Ji_1 = inj_res.inj_mods[i + 2]
@@ -155,10 +155,10 @@ function local_cohomology(M::SubquoModule{T}, I::MonoidAlgebraIdeal, i::Integer)
   end
 
   #get maps _phi: J^{i-1} -> J^i and _psi: J^i -> J^{i+1}
-  _phi = get_scalar_matrix(kQ, inj_res.cochain_maps[i])
+  _phi = get_scalar_matrix(kQ, inj_res.cochain_maps[i+1])
 
   if inj_res.upto > i
-    _psi = get_scalar_matrix(kQ, inj_res.cochain_maps[i + 1])
+    _psi = get_scalar_matrix(kQ, inj_res.cochain_maps[i + 2])
   else # map is zero 
     _psi = zero_matrix(k,length(Ji.indec_injectives), 1)
   end
@@ -419,7 +419,7 @@ function sector_partition(
       poly_tuple = intersect(_delta...)
       if dim(poly_tuple) < 0
         continue
-      elseif dim(poly_tuple) == 0 && length(lattice_points(poly_tuple)) == 0
+      elseif dim(poly_tuple) == 0 && is_bounded(poly_tuple) && length(lattice_points(poly_tuple)) == 0
         continue
       end
 
@@ -460,9 +460,9 @@ function _local_cohomology_sector(
   _A = [A_0, A_1, A_2]
 
   # define vector spaces J_{S_A0}, J_{S_A1} and J_{S_A2}
-  F_0 = free_module(field, length(A_0))
-  F_1 = free_module(field, length(A_1))
-  F_2 = free_module(field, length(A_2))
+  F_0 = vector_space(field, length(A_0))
+  F_1 = vector_space(field, length(A_1))
+  F_2 = vector_space(field, length(A_2))
 
   #compute the maps by deleting rows and columns in phi and psi
   #phi
diff --git a/experimental/InjectiveResolutions/test/local_cohomology_hartshorne_example.jl b/experimental/InjectiveResolutions/test/local_cohomology_hartshorne_example.jl
index 03ed8d8a13ce..0119e39d5ea0 100644
--- a/experimental/InjectiveResolutions/test/local_cohomology_hartshorne_example.jl
+++ b/experimental/InjectiveResolutions/test/local_cohomology_hartshorne_example.jl
@@ -16,13 +16,13 @@
 
     # cohomological degree 1
     H1 = Oscar.local_cohomology(I_M, I, 1)
-    H1_sectors = [h for h in H1.sectors if dim(h.H)>0] #sectors with non-zero local cohomomology
+    H1_sectors = [h for h in H1.sectors if !is_zero(h)] #sectors with non-zero local cohomomology
     @test !Oscar.is_zero(H1)
     @test length(H1_sectors) == 1 
 
     # cohomological degree 2 
     H2 = Oscar.local_cohomology(I_M, I, 2)
-    H2_sectors = [h for h in H2.sectors if dim(h.H)>0] #sectors with non-zero local cohomology
+    H2_sectors = [h for h in H2.sectors if !is_zero(h)] #sectors with non-zero local cohomology
     @test !Oscar.is_zero(H2)
     @test length(H2_sectors) == 1