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Intangible assets and goodwill - Indefinite-lived Intangibles (Details) - USD ($)
$ in Thousands
9 Months Ended
Sep. 30, 2023
Dec. 31, 2022
Indefinite-lived intangibles    
Impairment $ (217,800)  
Intangible assets, net 423,342 $ 705,891
PTC-FA and PTC-AS    
Indefinite-lived intangibles    
Impairment (217,800)  
Indefinite-lived intangible assets    
Indefinite-lived intangibles    
Beginning Balance 453,566  
Additions  
Impairment (217,800)  
Ending Balance 235,766  
Intangible assets, net 423,342  
Indefinite-lived intangible assets | Upstaza    
Indefinite-lived intangibles    
Beginning Balance 235,766  
Additions  
Ending Balance 235,766  
Indefinite-lived intangible assets | PTC-FA and PTC-AS    
Indefinite-lived intangibles    
Impairment (217,800)  
Indefinite-lived intangible assets | PTC-FA    
Indefinite-lived intangibles    
Beginning Balance 112,500  
Additions  
Impairment (112,500)  
Indefinite-lived intangible assets | PTC-AS    
Indefinite-lived intangibles    
Beginning Balance 105,300  
Additions  
Impairment $ (105,300)