https://msdn.microsoft.com/en-za/library/ms189799.aspx
Permissions
To create a DML trigger requires ALTER permission on the table or view on which the trigger is being created.
To create a DDL trigger with server scope (ON ALL SERVER) or a logon trigger requires CONTROL SERVER permission on the server. To create a DDL trigger with database scope (ON DATABASE) requires ALTER ANY DATABASE DDL TRIGGER permission in the current database.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability