Hirokado, Masayuki A non-liftable Calabi-Yau threefold in characteristic 3. (English) Zbl 0969.14028 Tohoku Math. J., II. Ser. 51, No. 4, 479-487 (1999). Summary: We show the existence of a Calabi-Yau threefold in characteristic 3 with its third Betti number zero. This example admits no lifting to characteristic zero and hence indicates that a theorem by Deligne that any \(K3\) surface in positive characteristic has a lifting to characteristic zero cannot be generalized straightforward to the case of Calabi-Yau threefolds. Cited in 1 ReviewCited in 20 Documents MSC: 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 14J30 \(3\)-folds 14G15 Finite ground fields in algebraic geometry Keywords:Calabi-Yau threefold; characteristic 3 PDFBibTeX XMLCite \textit{M. Hirokado}, Tôhoku Math. J. (2) 51, No. 4, 479--487 (1999; Zbl 0969.14028) Full Text: DOI References: [1] M ARTIN AND B MAZUR, Formal groups arising from algebraic varieties, Ann Sci Ecole Norm Sup. (4) 10 (1977), 87-131 · Zbl 0351.14023 [2] P DELIGNE, Relevement des surfaces K3 en caracteristique nulle, Lecture Notes in Math 868, Springer Verlag, 1981, 58-79 · Zbl 0495.14024 [3] T EKEDAHL, Foliations and inseparable morphisms, Proc. Sympos Pure Math 46, Part 2, Amer. Math Soc, Providence, RI, 1987, 139-149 · Zbl 0659.14018 [4] M HIROKADO, Zariski surfaces as quotients of Hirzebruch surfaces by 1-foliations, preprin · Zbl 1028.14006 [5] M HIROKADO, Calabi-Yau threefolds obtained as fiber products of elliptic andquasi-ellipticrational surfaces, to appear in J Pure Applied Algebra · Zbl 1048.14021 · doi:10.1016/S0022-4049(01)00022-6 [6] W LANG AND N NYGAARD, A short proof of the Rydakov-Safarevic theorem, Math Ann. 251 (1980), 171-173 · Zbl 0457.14018 · doi:10.1007/BF01536183 [7] Y MIYAOKA, Vector fields on Calabi-Yau manifolds in characteristic p, Daisuu Kikagaku Symposium a Kinosaki, 1995, 149-156. [8] N NYGAARD, On the fundamental group of a unirational 3-fold, Invent Math 44 (1978), 75-8 · Zbl 0427.14014 · doi:10.1007/BF01389903 [9] N NYGAARD, A p-aic proof of the non-existence of vectorfields on K3 surfaces, Ann of Math 110 (1979), 515-528 JSTOR: · Zbl 0448.14008 · doi:10.2307/1971236 [10] K. OGUISO, On certain rigid fibered Calabi-Yau threefolds, Math Z. 221 (1996), 437-44 · Zbl 0852.14012 · doi:10.1007/PL00004519 [11] A RUDAKOV AND I SHAFAREVICH, Inseparable morphisms of algebraic surfaces, Math USSR Izv. 1 (1976), 1205-1237 · Zbl 0379.14006 · doi:10.1070/IM1976v010n06ABEH001833 [12] A RUDAKOV AND I SHAFAREVICH, Surfaces of type K3 over fields of finite characteristics, J Soviet Mat 22(1983), 1476-1533. · Zbl 0518.14015 [13] K. SAKAMAKI, Artin-Mazur formal groups and Picard-Fuchs equations attached to certain Calabi-Yau three folds, Master’s Thesis, Kyoto University, 1994 [14] J SERRE, Sur la topologie des varietes algebriques en caracteristique p, Symposium Internacionalde Topolo gia Algebraica, Mexico, 1958, 24-53. · Zbl 0098.13103 [15] N SUWA, Hodge-Witt cohomology of complete intersections, J. Math. Soc.Japan 45 (1993), 295-30 · Zbl 0815.14013 · doi:10.2969/jmsj/04520295 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.