Production method for olefin-based polymer, olefin polymerization catalyst, and olefin-based polymer

A production method for polypropylene, the production method comprising polymerizing propylene in the presence of the following components (A) to (D):

• (A) a transition metal compound;
• (B) a boron compound capable of forming an ion pair with the component (A);
• (C) an organoaluminum compound;
• and
• (D) water,
• wherein:
• a molar ratio [(D)/(A)] of a molar quantity of the component (D) to a molar quantity of a transition metal in the component (A) is 5 or more and 10,000 or less;
• a molar ratio [(D)/(C)] of the molar quantity of the component (D) to a molar quantity of an aluminum atom in the component C) is more than 0 and 0.9 or less;
• the transition metal compound (A) is a double crosslinked metallocene complex represented by a formula (I):
• M represents a metal element of Groups 3 to 10 of the periodic table or the lanthanoid series;
• E1 and E2 each represent a ligand selected from a substituted cyclopentadienyl group, an indenyl group, a substituted indenyl group, a heterocyclopentadienyl group, a substituted heterocyclopentadienyl group, an amide group, a phosphide group, a hydrocarbon group, and a silicon-containing group, form a crosslinked structure via A1 and A2, and may be identical to or different from each other;
• X represents a σ-bonding ligand, and when a plurality of X's are present, the plurality of X's may be identical to or different from each other, and X may be crosslinked with any other X, E1, E2, or Y;
• Y represents a Lewis base, and when a plurality of Y's are present, the plurality of Y's may be identical to or different from each other, and Y may be crosslinked with any other Y, E1, E2, or X;
• A1 and A2 each represent a divalent crosslinking group for bonding two ligands, and each represent a hydrocarbon group having 1 to 20 carbon atoms, a halogen-containing hydrocarbon group having 1 to 20 carbon atoms, a silicon-containing group, a germanium-containing group, a tin-containing group, —O—, —CO—, —S—, —SO2—, —Se—, —NR1—, —PR1—, —P(O)R1—, —BR1—, or —AlR1—, wherein R1 represents a hydrogen atom, a halogen atom, a hydrocarbon group having 1 to 20 carbon atoms, or a halogen-containing hydrocarbon group having 1 to 20 carbon atoms, and may be identical to or different from each other;
• q represents an integer of from 1 to 5 representing [(valence of M)-2];
• and
• r represents an integer of from 0 to 3.