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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 3, Pages 213–256 (Mi izv8754)  

On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci

S. G. Tankeev

Vladimir State University

Abstract: We prove that the Grothendieck standard conjecture $B(X)$ of Lefschetz type on the algebraicity of the operator $ ^{\mathrm{c}}\Lambda$ of Hodge theory is true for the fibre product $X=X_1\times_CX_2\times_CX_3$ of complex elliptic surfaces $X_k\to C$ over a smooth projective curve $C$ provided that the discriminant loci $\{\delta\in C\mid \operatorname{Sing}(X_{k\delta})\neq \varnothing\}$ $(k=1,2,3)$ are pairwise disjoint.

Keywords: standard conjecture, elliptic surface, fibre product, resolution of indeterminacies, Clemens–Schmid sequence, Gysin map.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00143
This paper was written with the financial support of the Russian Foundation for Basic Research (grant no. 18-01-00143).


DOI: https://doi.org/10.4213/im8754

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English version:
Izvestiya: Mathematics, 2019, 83:3, 613–653

Bibliographic databases:

UDC: 512.7
MSC: 14C25, 14C30, 14J27, 14J35
Received: 24.12.2017
Revised: 28.06.2018

Citation: S. G. Tankeev, “On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci”, Izv. RAN. Ser. Mat., 83:3 (2019), 213–256; Izv. Math., 83:3 (2019), 613–653

Citation in format AMSBIB
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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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