RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 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

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

Full text: PDF file (916 kB)
First page: PDF file
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 512.7
MSC: 14C25, 14C30, 14J27, 14J35
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
\Bibitem{Tan19} \by S.~G.~Tankeev \paper On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci \jour Izv. RAN. Ser. Mat. \yr 2019 \vol 83 \issue 3 \pages 213--256 \mathnet{http://mi.mathnet.ru/izv8754} \crossref{https://doi.org/10.4213/im8754} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2019IzMat..83..613T} \elib{http://elibrary.ru/item.asp?id=37652148} \transl \jour Izv. Math. \yr 2019 \vol 83 \issue 3 \pages 613--653 \crossref{https://doi.org/10.1070/IM8754} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000472863800008}