Personnel expenses and employee information - Personnel Expenses for All Payroll Employees (Detail) - EUR (€) € in Millions	12 Months Ended
Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Compensation Related Costs [Abstract]
Wages and salaries	€ 4,447.0	€ 3,502.5	€ 2,842.7
Social security expenses	410.5	300.7	249.8
Pension and retirement expenses	348.9	255.9	229.2
Share-based compensation expense	134.8	68.9	117.5
Personnel expenses	€ 5,341.2	€ 4,128.0	€ 3,439.2

No definition available.

Name:	us-gaap_CompensationRelatedCostsAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of expense for salary, wage, profit sharing; incentive and equity-based compensation; and other employee benefit.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(b)(4))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483621/220-10-S99-2

+ Details

Name:	us-gaap_LaborAndRelatedExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of labor-related expenses classified as other.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03.4)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483621/220-10-S99-2

+ Details

Name:	us-gaap_OtherLaborRelatedExpenses
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of cost (reversal of cost) for pension and other postretirement benefits.

+ References

No definition available.

+ Details

Name:	us-gaap_PensionAndOtherPostretirementBenefitExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of expense for salary and wage arising from service rendered by nonofficer and officer employees. Excludes allocated cost, labor-related nonsalary expense, and direct and overhead labor cost included in cost of good and service sold.

+ References

No definition available.

+ Details

Name:	us-gaap_SalariesWagesAndOfficersCompensation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of noncash expense for share-based payment arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (a)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-28

+ Details

Name:	us-gaap_ShareBasedCompensation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration