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Investments in Variable Interest Entities (Details) - USD ($)
$ in Millions
1 Months Ended 3 Months Ended 12 Months Ended
May 31, 2018
Oct. 31, 2017
Jun. 30, 2021
Jun. 30, 2020
Dec. 31, 2019
Dec. 31, 2021
Dec. 31, 2020
Dec. 31, 2019
Variable Interest Entity [Line Items]                
Potential future milestone payments commitment to third party approximately           $ 10,000.0    
Income (loss) from equity method investments           34.9 $ 3.3 $ (77.4)
Deferred tax asset, net     $ 490.0          
Deferred tax asset, gross     945.0          
Increase in unrecognized tax benefit     455.0          
Valuation allowance           1,961.3 1,753.9  
Investment in biotechnology companies that are determined to be unconsolidated variable interest entities           24.6 12.8  
ADUHELM                
Variable Interest Entity [Line Items]                
Valuation allowance           $ 390.0    
Neurimmune                
Variable Interest Entity [Line Items]                
Term of collaboration agreement           12 years    
Research and development costs, percentage           100.00%    
Payment to Neurimmune $ 50.0 $ 150.0            
Reduction in royalty rate payable on commercial sales   15.00%            
Additional reduction in royalty rate payable on commercial sales 5.00%              
Regulatory Milestones                
Variable Interest Entity [Line Items]                
Potential future milestone payments commitment to third party approximately           $ 900.0    
Regulatory Milestones | Neurimmune                
Variable Interest Entity [Line Items]                
Potential future milestone payments commitment to third party approximately       $ 75.0        
Eisai                
Variable Interest Entity [Line Items]                
Income (loss) from equity method investments       $ 33.8 $ 33.8 $ 45.0 $ 33.8 $ 0.0
Percentage of future development costs           45.00%    
Eisai | ADUHELM                
Variable Interest Entity [Line Items]                
Income (loss) from equity method investments     45.0     $ 45.0    
Eisai | Twelve months | ADUHELM                
Variable Interest Entity [Line Items]                
Potential future milestone payments commitment to third party approximately           100.0    
Eisai | Regulatory Milestones | European Union | ADUHELM                
Variable Interest Entity [Line Items]                
Potential future milestone payments commitment to third party approximately           50.0    
Eisai | Regulatory Milestones | JAPAN | ADUHELM                
Variable Interest Entity [Line Items]                
Potential future milestone payments commitment to third party approximately           $ 50.0    
Eisai | Regulatory Milestones | Neurimmune | ADUHELM                
Variable Interest Entity [Line Items]                
Potential future milestone payments commitment to third party approximately     $ 100.0