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:
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