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Proceedings of the London Mathematical Society Advance Access originally published online on May 7, 2009
Proceedings of the London Mathematical Society 2009 99(3):725-756; doi:10.1112/plms/pdp015
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© 2009 London Mathematical Society

Building blocks of étale endomorphisms of complex projective manifolds

Noboru Nakayama

Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502
Japan
nakayama@kurims.kyoto-u.ac.jp

De-Qi Zhang

Department of Mathematics
National University of Singapore
2 Science Drive 2
Singapore 117543
Singapore

Received 13 May 2008. Revision received 13 January 2009.

Étale endomorphisms of complex projective manifolds are constructed from two building blocks up to isomorphism if the good minimal model conjecture is true. They are the endomorphisms of abelian varieties and the nearly étale rational endomorphisms of weak Calabi–Yau varieties.

2000 Mathematics Subject Classification 14E20, 14E07, 32H50.

The first author was partly supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science. The second author was supported by an ARF of NUS.


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