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              Abstract
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 We prove various counting formulas for CM-types of CM-fields and use them to
 construct infinite families of degenerate CM-types.
  
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              Keywords
              
                CM-types, degenerate CM-types, Hodge conjecture
               
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              Mathematical Subject Classification 2010
              
                Primary: 11G15, 14K22
               
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              Milestones
              
                Received: 14 March 2019
               
              
                Revised: 17 May 2019
               
              
                Accepted: 31 May 2019
               
              
                Published: 11 October 2019
               
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