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Income taxes - Reconciliation of the Provision (Benefit) for Income Taxes (Details) - USD ($)
$ in Millions
 12 Months Ended
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)