Journal of the Ramanujan Mathematical Society

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Manin Problems for Shimura Varieties of Hodge Type


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

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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.
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  • Manin Problems for Shimura Varieties of Hodge Type

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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.