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Shareholders' equity - Purchase of Equity Securities (Details) - EUR (€) € / shares in Units, € in Millions	1 Months Ended												2 Months Ended	3 Months Ended	4 Months Ended	5 Months Ended	6 Months Ended	7 Months Ended	8 Months Ended	9 Months Ended	10 Months Ended	11 Months Ended	12 Months Ended
	Dec. 31, 2025	Nov. 30, 2025	Oct. 31, 2025	Sep. 30, 2025	Aug. 31, 2025	Jul. 31, 2025	Jun. 30, 2025	May 31, 2025	Apr. 30, 2025	Mar. 31, 2025	Feb. 28, 2025	Jan. 31, 2025	Feb. 28, 2025	Mar. 31, 2025	Apr. 30, 2025	May 31, 2025	Jun. 30, 2025	Jul. 31, 2025	Aug. 31, 2025	Sep. 30, 2025	Oct. 31, 2025	Nov. 30, 2025	Dec. 31, 2025	Dec. 31, 2024
Equity [Abstract]
Total number of shares purchased (in shares)	580,630	816,582	483,439	0	0	200,024	385,453	398,170	1,390,673	2,067,246	1,819,703	181,400	2,001,103	4,068,349	5,459,022	5,857,192	6,242,645	6,442,669	6,442,669	6,442,669	6,926,108	7,742,690	8,323,320	574,925
Average price paid per share (Euro per share)	€ 934.45	€ 885.88	€ 897.81	€ 0	€ 0	€ 676.40	€ 669.72	€ 648.62	€ 583.36	€ 658.42	€ 712.36	€ 714.60											€ 714.86
Maximum value of shares that may yet be purchased (€ millions)	€ 4,350.0	€ 4,892.6	€ 5,616.0	€ 6,050.0	€ 6,050.0	€ 6,050.0	€ 6,185.3	€ 6,443.4	€ 6,701.7	€ 7,513.0	€ 8,874.1	€ 10,170.4

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Average price paid per share of shares purchased under the repurchase program.

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- Definition

Maximum Value Of Shares That May Yet Be Purchased Under Program

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- Definition

Number of shares that have been repurchased during the period and are being held in treasury.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-2

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480008/505-10-S99-1

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