On a duality theorem for abelian varieties over higher dimensional local fields. (English) Zbl 1101.14307
Summary: We prove a duality theorem of abelian varieties over higher dimensional local fields under some conditions. It might be a sort of generalization of the classical Tate duality theorem of abelian varieties over local fields.
MSC:
14G20 | Local ground fields in algebraic geometry |
14K15 | Arithmetic ground fields for abelian varieties |
11G10 | Abelian varieties of dimension \(> 1\) |
11S31 | Class field theory; \(p\)-adic formal groups |
Keywords:
duality theorem of Galois cohomology groups related to abelian varieties; higher dimensional local fields; Weil-Barsotti formula; higher Tate dualityReferences:
[1] | B. KAHN, The decomposable part of motivic cohomology and bijectivity of the norm residue homomorphism, Contemp. Math., 126 (1992), 79-87 · Zbl 0759.19005 |
[2] | K. KATO, A generalization of local class field theory by using A-groups I, J. Fac. Sci. Univ Tokyo Sect. IA Math., 26 (1979), 303-376. · Zbl 0428.12013 |
[3] | K. KATO, A generalization of local class field theory by using A’-groups II, J. Fac. Sci. Univ Tokyo Sect. IA Math, 27 (1980), 603-683. · Zbl 0463.12006 |
[4] | K. KATO, Galois cohomology of complete discrete valuation fields, Algebraic Vheory, Lecture. Note in Math, 967, Springer-Verlag, (1980), 215-238 · Zbl 0506.12022 |
[5] | Y. KOYA, A generalization of class formation by using hypercohomology, Invent. Math, 10 (1990), 705-715. · Zbl 0751.11055 · doi:10.1007/BF01231522 |
[6] | J. S. MILNE, Arithmetic Duality Theorems, Academic Press, 1986 · Zbl 0613.14019 |
[7] | J. SERRE, Groupes Algebques et Corps de Classes, Hermann, Pans, 1959 · Zbl 0097.35604 |
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.