Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Hodge Structures of CM-Type


Affiliations
1 Department of Mathematics, East Carolina University, Greenville, NC 27858, United States
     

   Subscribe/Renew Journal


We show that any effective Hodge structure of CM-type occurs (without having to take a Tate twist) in the cohomology of some CM abelian variety over C. As a consequence we get a simple proof of the theorem (due to Hazama) that the usual Hodge conjecture for the class of all CM abelian varieties implies the general Hodge conjecture for the same class.
User
Subscription Login to verify subscription
Notifications
Font Size

Abstract Views: 227

PDF Views: 0




  • Hodge Structures of CM-Type

Abstract Views: 227  |  PDF Views: 0

Authors

Salman Abdulali
Department of Mathematics, East Carolina University, Greenville, NC 27858, United States

Abstract


We show that any effective Hodge structure of CM-type occurs (without having to take a Tate twist) in the cohomology of some CM abelian variety over C. As a consequence we get a simple proof of the theorem (due to Hazama) that the usual Hodge conjecture for the class of all CM abelian varieties implies the general Hodge conjecture for the same class.