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Income Taxes - Narrative (Details) - USD ($)
$ in Millions
 12 Months Ended
Dec. 31, 2020
Dec. 31, 2019
Dec. 31, 2018
Dec. 31, 2017
Tax Credit Carryforward [Line Items]        
GILTI $ (1,143.7) $ (1,381.6)    
Income taxes paid 62.0      
Deferred tax liabilities, temporary differences, purchase accounting, foreign subsidiaries 1,500.0      
Total deferred charges and prepaid taxes 142.2 243.8    
Valuation allowance 1,753.9 1.1    
Other 103.1 103.7    
Unrecognized tax benefit 68.8 122.7 $ 109.1  
Net interest expense 1.0 4.7 2.2  
Unrecognized tax benefits, interest on income taxes accrued 21.2 20.0    
Decrease in unrecognized tax benefits is reasonably possible 25.0      
2017 Tax Act        
Tax Credit Carryforward [Line Items]        
Reduction in deferred tax liability, undistributed foreign earnings     34.6  
Income tax expense (benefit)     12.7  
GILTI     135.8  
Other tax expense (benefit)     $ 11.0  
Transition toll tax liabilities 697.0 697.0    
General Business | Domestic Country        
Tax Credit Carryforward [Line Items]        
Operating loss carryforwards 0.6      
Tax credit carryforward, amount 1.3      
Operating loss carryforward, subject to expiration 18,000.0      
General Business | Foreign Tax Authority        
Tax Credit Carryforward [Line Items]        
Operating loss carryforward, subject to expiration 16,800.0      
Research | State and Local Jurisdiction        
Tax Credit Carryforward [Line Items]        
Tax credit carryforward, amount 142.4      
Earnings in the form of cash and cash equivalents | 2017 Tax Act        
Tax Credit Carryforward [Line Items]        
Transition toll tax repatriation tax rate       15.50%
Other Foreign Earnings | 2017 Tax Act        
Tax Credit Carryforward [Line Items]        
Transition toll tax repatriation tax rate       8.00%
Minimum        
Tax Credit Carryforward [Line Items]        
Residual U.S. tax liability on reversal of deferred tax liabilities on foreign subsidiaries purchase accounting 300.0      
Maximum        
Tax Credit Carryforward [Line Items]        
Residual U.S. tax liability on reversal of deferred tax liabilities on foreign subsidiaries purchase accounting 400.0      
Denmark Manufacturing Operations        
Tax Credit Carryforward [Line Items]        
Tax expense on disposal group   68.9    
TECFIDERA        
Tax Credit Carryforward [Line Items]        
Deferred tax assets, value, reduction in value 1,700.0      
Deferred tax liabilities, value, reduction in value 1,600.0      
Income tax expense, reduction in deferred tax assets and liabilities, net $ 90.3      
Intellectual Property        
Tax Credit Carryforward [Line Items]        
Other   754.1    
Deferred tax liabilities, other   $ 603.3