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June 2020 Grothendieck’s pairing on Néron component groups: Galois descent from the semistable case
Takashi Suzuki
Kyoto J. Math. 60(2): 593-716 (June 2020). DOI: 10.1215/21562261-2019-0045

Abstract

In our previous study of duality for complete discrete valuation fields with perfect residue field, we treated coefficients in finite flat group schemes. In this paper, we treat abelian varieties. This, in particular, implies Grothendieck’s conjecture on the perfectness of his pairing between the Néron component groups of an abelian variety and its dual. The point is that our formulation is well suited to Galois descent. From the known case of semistable abelian varieties, we deduce the perfectness in full generality. We also treat coefficients in tori and, more generally, 1-motives.

Citation

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Takashi Suzuki. "Grothendieck’s pairing on Néron component groups: Galois descent from the semistable case." Kyoto J. Math. 60 (2) 593 - 716, June 2020. https://doi.org/10.1215/21562261-2019-0045

Information

Received: 23 April 2015; Revised: 9 December 2017; Accepted: 22 December 2017; Published: June 2020
First available in Project Euclid: 2 April 2020

zbMATH: 07223247
MathSciNet: MR4094746
Digital Object Identifier: 10.1215/21562261-2019-0045

Subjects:
Primary: 11G10
Secondary: 11S25, 14F20

Rights: Copyright © 2020 Kyoto University

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Vol.60 • No. 2 • June 2020
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