Share-based compensation - Performance Shares Activity (Details) - Performance shares	12 Months Ended
Dec. 31, 2024 $ / shares shares	Dec. 31, 2024 € / shares shares	Dec. 31, 2023 $ / shares shares	Dec. 31, 2023 € / shares shares	Dec. 31, 2022 $ / shares shares	Dec. 31, 2022 € / shares shares
Number of shares
Outstanding at beginning of year (in shares)	9,816,619	9,816,619
Granted (in shares)	1,856,679	1,856,679
Forfeited (in shares)	(294,689)	(294,689)
Vested (in shares)	(3,080,029)	(3,080,029)	(2,985,299)	(2,985,299)	(3,084,926)	(3,084,926)
Outstanding at end of year (in shares)	8,298,580	8,298,580	9,816,619	9,816,619
Weighted average grant date fair value
Outstanding at beginning of year (in usd or eur per share) \| (per share)	$ 41.56	€ 37.90
Granted (in usd or eur per share) \| (per share)	79.52	73.85	$ 48.55	€ 45.57	$ 36.29	€ 34.50
Forfeited (in usd or eur per share) \| (per share)	46.12	41.44
Vested (in usd or eur per share) \| (per share)	40.93	34.97
Outstanding at beginning of year (in usd or eur per share) \| (per share)	$ 50.11	€ 46.89	$ 41.56	€ 37.90

The number of equity-based payment instruments, excluding stock (or unit) options, that were forfeited during the reporting period.

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- Definition

Weighted average fair value as of the grant date of equity-based award plans other than stock (unit) option plans that were not exercised or put into effect as a result of the occurrence of a terminating event.

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- Definition

The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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- Definition

The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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- Definition

The number of non-vested equity-based payment instruments, excluding stock (or unit) options, that validly exist and are outstanding as of the balance sheet date.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(ii)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

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- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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- Definition

Per share or unit weighted-average fair value of nonvested award under share-based payment arrangement. Excludes share and unit options.

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+ Details

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- Definition

The number of equity-based payment instruments, excluding stock (or unit) options, that vested during the reporting period.

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+ Details

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- Definition

The weighted average fair value as of grant date pertaining to an equity-based award plan other than a stock (or unit) option plan for which the grantee gained the right during the reporting period, by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash in accordance with the terms of the arrangement.

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