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Share-based compensation - Expenses (Details) - EUR (€) € in Millions	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Share-Based Payment Arrangement [Abstract]
Incurred expenses	€ 172.6	€ 134.8	€ 68.9
Expected expenses of conditionally granted plans in future periods	€ 246.1	€ 187.2	€ 113.0
Weighted average period for recognizing these expected expenses	1 year 6 months	1 year 7 months 6 days	1 year 4 months 24 days
Recognized income tax benefit (excluding excess income tax benefits)	€ 28.2	€ 16.3	€ 10.2

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Amount of cost not yet recognized for nonvested award under share-based payment arrangement.

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

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Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

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

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Amount of tax benefit for recognition of expense of award under share-based payment arrangement.

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Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
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-Publisher FASB
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Amount of noncash expense for share-based payment arrangement.

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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
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