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

Manin Problems for Shimura Varieties of Hodge Type


Affiliations
1 Department of Mathematical Sciences, Binghamton University, Binghamton, P. O. Box 6000, New York-13902-6000, United States
     

   Subscribe/Renew Journal


Let k be a perfect field of characteristic p>0. We prove the existence of ascending and descending slope filtrations for Shimura p-divisible objects over k. We use them to classify rationally these objects over ̅k. Among geometric applications, we mention two. First we formulate Manin problems for Shimura varieties of Hodge type. We solve them if either p≥3 or p=2 and two mild conditions hold. Second we formulate integral Manin problems. We solve them for certain Shimura varieties of PEL type.
User
Subscription Login to verify subscription
Notifications
Font Size

Abstract Views: 151

PDF Views: 0




  • Manin Problems for Shimura Varieties of Hodge Type

Abstract Views: 151  |  PDF Views: 0

Authors

Adrian Vasiu
Department of Mathematical Sciences, Binghamton University, Binghamton, P. O. Box 6000, New York-13902-6000, United States

Abstract


Let k be a perfect field of characteristic p>0. We prove the existence of ascending and descending slope filtrations for Shimura p-divisible objects over k. We use them to classify rationally these objects over ̅k. Among geometric applications, we mention two. First we formulate Manin problems for Shimura varieties of Hodge type. We solve them if either p≥3 or p=2 and two mild conditions hold. Second we formulate integral Manin problems. We solve them for certain Shimura varieties of PEL type.