summary of significant accounting policies - Useful lives intangible assets (Details)	12 Months Ended
	Dec. 31, 2021
Customer contracts and related customer relationships | Minimum
Useful Lives of Intangible Assets Other Than Goodwill
Estimated useful lives of purchased intangible assets other than goodwill	4 years
Customer contracts and related customer relationships | Maximum
Useful Lives of Intangible Assets Other Than Goodwill
Estimated useful lives of purchased intangible assets other than goodwill	15 years
Fixed subscriber base
Useful Lives of Intangible Assets Other Than Goodwill
Estimated useful lives of purchased intangible assets other than goodwill	25 years
Software | Minimum
Useful Lives of Intangible Assets Other Than Goodwill
Estimated useful lives of purchased intangible assets other than goodwill	2 years
Software | Maximum
Useful Lives of Intangible Assets Other Than Goodwill
Estimated useful lives of purchased intangible assets other than goodwill	10 years
Access to rights-of-way, crowdsource assets and other | Minimum
Useful Lives of Intangible Assets Other Than Goodwill
Estimated useful lives of purchased intangible assets other than goodwill	5 years
Access to rights-of-way, crowdsource assets and other | Maximum
Useful Lives of Intangible Assets Other Than Goodwill
Estimated useful lives of purchased intangible assets other than goodwill	30 years