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Post-employment benefits - Assumptions used for defined benefit obligations (Detail)
Dec. 31, 2023
Dec. 31, 2022
Post-employment benefits [Line Items]    
Actuarial assumption of discount rates 4.30% 4.70%
Actuarial assumption of expected rates of inflation 2.20% 2.20%
Actuarial assumption of expected rates of salary increases 3.00% 2.90%
Germany [Member]    
Post-employment benefits [Line Items]    
Actuarial assumption of discount rates 3.70% 4.10%
Actuarial assumption of expected rates of inflation 2.00% 2.00%
Actuarial assumption of expected rates of salary increases 2.80% 2.80%
United States of America [Member]    
Post-employment benefits [Line Items]    
Actuarial assumption of discount rates 5.00% 5.20%
Actuarial assumption of expected rates of inflation 2.30% 2.30%
Actuarial assumption of expected rates of salary increases 0.00% 0.00%
Other countries [Member]    
Post-employment benefits [Line Items]    
Actuarial assumption of discount rates 4.90% 4.90%
Actuarial assumption of expected rates of inflation 2.50% 2.60%
Actuarial assumption of expected rates of salary increases 4.30% 3.30%