Description of the business and summary of significant accounting policies: - Property and equipment (Details)	Dec. 31, 2025
Indefeasible rights of use (IRUs)
Description of the business and summary of significant accounting policies:
Property, Plant, and Equipment, Useful Life, Term, Description [Extensible Enumeration]	us-gaap:UsefulLifeShorterOfTermOfLeaseOrAssetUtilityMember
Minimum | Indefeasible rights of use (IRUs)
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	15 years
Maximum | Indefeasible rights of use (IRUs)
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	20 years
Network equipment | Minimum
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	2 years
Network equipment | Maximum
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	8 years
Leasehold improvements
Description of the business and summary of significant accounting policies:
Property, Plant, and Equipment, Useful Life, Term, Description [Extensible Enumeration]	us-gaap:UsefulLifeShorterOfTermOfLeaseOrAssetUtilityMember
Software | Minimum
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	5 years
Software | Maximum
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	10 years
Owned buildings | Minimum
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	16 years
Owned buildings | Maximum
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	40 years
Office and other equipment | Minimum
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	2 years
Office and other equipment | Maximum
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	7 years
Asset retirement obligations
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	4 years
System infrastructure | Minimum
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	5 years
System infrastructure | Maximum
Description of the business and summary of significant accounting policies:
Depreciation or amortization period (in years)	40 years