Motives of isogenous K3 surfaces

被引：20

作者：

Huybrechts, Daniel ^{[1
]}

机构：

[1] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

来源：

COMMENTARII MATHEMATICI HELVETICI | 2019年 / 94卷 / 03期

关键词：

K3; surfaces; derived categories; motives; Hodge conjecture; Brauer groups; twisted K3 surfaces; EQUIVALENCES;

D O I：

10.4171/CMH/465

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that isogenous K3 surfaces have isomorphic Chow motives. This provides a motivic interpretation of a long standing conjecture of Safarevic which has been settled only recently by Buskin. The main step consists of a new proof of Safarevic's conjecture that circumvents the analytic parts in [2], avoiding twistor spaces and non-algebraic K3 surfaces.

引用

页码：445 / 458

页数：14

共 21 条

[1]

Andre Y., 2005, ASTERISQUE, V2003, P115

[2]

Buskin N., CRELLE J REINE ANGEW

[3] Twisted Fourier-Mukai functors [J].

Canonaco, Alberto ;

Stellari, Paolo .

ADVANCES IN MATHEMATICS, 2007, 212 (02) :484-503

[4] Derived categories of coherent sheaves and motives of K3 surfaces [J].

Del Padrone, Alessio ;

Pedrini, Claudio .

REGULATORS, 2012, 571 :219-232

[5] Some remarks on L-equivalence of algebraic varieties [J].

Efimov, Alexander I. .

SELECTA MATHEMATICA-NEW SERIES, 2018, 24 (04) :3753-3762

[6] Cremona transformations and derived equivalences of K3 surfaces [J].

Hassett, Brendan ;

Lai, Kuan-Wen .

COMPOSITIO MATHEMATICA, 2018, 154 (07) :1508-1533

[7] Equivalences of twisted K3 surfaces [J].

Huybrechts, D ;

Stellari, P .

MATHEMATISCHE ANNALEN, 2005, 332 (04) :901-936

[8] Motives of derived equivalent K3 surfaces [J].

Huybrechts, D. .

ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2018, 88 (01) :201-207

[9] Generalized Calabi-Yau structures, K3 surfaces, and B-fields [J].

Huybrechts, D .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2005, 16 (01) :13-36

[10]

Huybrechts D, 2016, CAMBRIDGE STUDIES AD, V158

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