Ordinary K3 surfaces over a finite field
2020 ◽
Vol 2020
(761)
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pp. 141-161
Keyword(s):
AbstractWe give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over {{\mathbf{Z}}}. This gives an analogue for K3 surfaces of Deligne’s description of the category of ordinary abelian varieties over a finite field, and refines earlier work by N.O. Nygaard and J.-D. Yu. Our main result is conditional on a conjecture on potential semi-stable reduction of K3 surfaces over p-adic fields. We give unconditional versions for K3 surfaces of large Picard rank and for K3 surfaces of small degree.
2018 ◽
Vol 556
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pp. 421-427
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2010 ◽
Vol 06
(03)
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pp. 579-586
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2003 ◽
Vol 55
(2)
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pp. 225-246
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2005 ◽
Vol 15
(03)
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pp. 467-502
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1998 ◽
Vol 132
(2)
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pp. 179-193
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2007 ◽
Vol 10
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pp. 307-328
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