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Income taxes - Reconciliation of the Provision (Benefit) for Income Taxes (Details) - USD ($) $ in Millions | 12 Months Ended
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Dec. 31, 2023 | Dec. 31, 2022 | Dec. 31, 2021
Income Tax Disclosure [Abstract] |  |  |
United States statutory income tax benefit | $ (73.0) | $ (13.2) | $ (96.9)
Income and losses for which no provision or benefit has been recognized | 123.2 | 40.9 | 91.1
Foreign rate differential and other foreign tax expense | 12.7 | 6.4 | 0.4
Income tax withholdings | 14.0 | 19.7 | 13.5
Permanent items | (3.0) | (2.1) | (1.8)
Change in uncertain tax positions | 3.8 | 0.4 | (0.3)
Change in valuation allowances | 2.1 | (9.8) | (0.8)
U.S. income tax benefit | (0.6) | 0.0 | 0.0
Other | 0.1 | 0.0 | 0.0
Enacted rate changes | 0.0 | 0.0 | (17.1)
Total provision (benefit) for income taxes | $ 79.3 | $ 42.3 | $ (11.9)

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- Definition Amount of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 250 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 8 -Publisher FASB -URI https://asc.fasb.org//1943274/2147483443/250-10-50-8 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 250 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 9 -Publisher FASB -URI https://asc.fasb.org//1943274/2147483443/250-10-50-9 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 10 -Publisher FASB -URI https://asc.fasb.org//1943274/2147482685/740-10-50-10 Reference 4: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SAB TOPIC 6.I.7) -Publisher FASB -URI https://asc.fasb.org//1943274/2147479360/740-10-S99-1 Reference 5: http://www.xbrl.org/2003/role/disclosureRef -Topic 280 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 22 -Subparagraph (h) -Publisher FASB -URI https://asc.fasb.org//1943274/2147482810/280-10-50-22 Reference 6: http://www.xbrl.org/2003/role/disclosureRef -Topic 944 -SubTopic 220 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.7-04(9)) -Publisher FASB -URI https://asc.fasb.org//1943274/2147483586/944-220-S99-1 Reference 7: http://www.xbrl.org/2003/role/disclosureRef -Name Accounting Standards Codification -Section 45 -Paragraph 2 -Subparagraph (a) -SubTopic 20 -Topic 740 -Publisher FASB -URI https://asc.fasb.org//1943274/2147482659/740-20-45-2 Reference 8: http://www.xbrl.org/2003/role/disclosureRef -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.4-08(h)) -SubTopic 10 -Topic 235 -Publisher FASB -URI https://asc.fasb.org//1943274/2147480678/235-10-S99-1 + Details
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