Income taxes - Reconciliation of Beginning and Ending Balance of Liability for Unrecognized Tax Benefits (Details) - EUR (€) € in Millions	12 Months Ended
Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Unrecognized Tax Benefits [Roll Forward]
Balance as at January 1	€ (193.6)	€ (160.0)	€ (144.3)
Gross increases – tax positions in prior period	(39.7)	(44.1)	(11.7)
Gross decreases – tax positions in prior period	11.0	12.6	2.0
Gross increases – tax positions in current period	(64.9)	(27.7)	(23.1)
Settlements	69.9	2.2	6.8
Lapse of statute of limitations	6.1	17.9	13.2
Effect of changes in exchange rates	(2.8)		(2.9)
Effect of changes in exchange rates		5.5
Total liability for unrecognized tax benefits	(214.0)	(193.6)	(160.0)
Balance of accrued interest and penalties	(39.1)	(56.1)	(55.5)
Total liability for unrecognized tax benefits	€ (253.1)	€ (249.7)	€ (215.5)

Unrecognized Tax Benefits Excluding Interest and Penalties

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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.

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- Definition

Amount of unrecognized tax benefits.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 217
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482663/740-10-55-217

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 15A
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-15A

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 10B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482525/740-10-45-10B

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- Definition

Amount of decrease in unrecognized tax benefits resulting from foreign currency translation.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 15A
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-15A

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- Definition

Amount of decrease in unrecognized tax benefits resulting from tax positions taken in prior period tax returns.

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Amount of decrease in unrecognized tax benefits resulting from settlements with taxing authorities.

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- Definition

Amount accrued for interest on an underpayment of income taxes and penalties related to a tax position claimed or expected to be claimed in the tax return.

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- Definition

Amount of increase in unrecognized tax benefits resulting from tax positions that have been or will be taken in current period tax return.

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Amount of increase in unrecognized tax benefits resulting from foreign currency translation.

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Amount of increase in unrecognized tax benefits resulting from tax positions taken in prior period tax returns.

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Amount of decrease in unrecognized tax benefits resulting from lapses of applicable statutes of limitations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 15A
-Subparagraph (a)(4)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-15A

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