[Conditions cohomologiques sur les endomorphismes des variétés projectives]
We characterize possible periodic subvarieties for surjective endomorphisms of complex abelian varieties in terms of the eigenvalues of the cohomological actions induced by the endomorphisms, extending previous work in this direction by Pink and Roessler [20]. By applying our characterization to induced endomorphisms of Albanese varieties, we draw conclusions about the dynamics of surjective endomorphisms for a broad class of projective varieties. We also analyze several classes of surjective endomorphisms that are distinguished by properties of their cohomological actions.
Pour des endomorphismes surjectives sur des variétés abéliennes complexes, nous décrivons les sous-variétés périodiques quit peuvent se présenter au moyens des valeurs propres des actions cohomologiques des endomorphismes. Cette entreprise élargit quelques idées des Pink et Roessler [20]. Nous utilisons ensuite la description des sous-variétés périodiques en étudiant des endomorphismes sur des variétés d’Albanese qui viennent des endomorphismes sur des sous-variétés. Nous aussi définissons et étudions quelques catégories des endomorphismes qui se différencient par certaines propriétés de leurs actions cohomologiques.
Krieger, Holly 1 ; Reschke, Paul 1
@article{BSMF_2017__145_3_449_0,
author = {Krieger, Holly and Reschke, Paul},
title = {Cohomological {Conditions} on {Endomorphisms} of {Projective} {Varieties}},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
pages = {449--468},
year = {2017},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {145},
number = {3},
doi = {10.24033/bsmf.2744},
mrnumber = {3766117},
zbl = {1387.32022},
language = {en},
url = {https://numdam.org/articles/10.24033/bsmf.2744/}
}
TY - JOUR AU - Krieger, Holly AU - Reschke, Paul TI - Cohomological Conditions on Endomorphisms of Projective Varieties JO - Bulletin de la Société Mathématique de France PY - 2017 SP - 449 EP - 468 VL - 145 IS - 3 PB - Société mathématique de France UR - https://numdam.org/articles/10.24033/bsmf.2744/ DO - 10.24033/bsmf.2744 LA - en ID - BSMF_2017__145_3_449_0 ER -
%0 Journal Article %A Krieger, Holly %A Reschke, Paul %T Cohomological Conditions on Endomorphisms of Projective Varieties %J Bulletin de la Société Mathématique de France %D 2017 %P 449-468 %V 145 %N 3 %I Société mathématique de France %U https://numdam.org/articles/10.24033/bsmf.2744/ %R 10.24033/bsmf.2744 %G en %F BSMF_2017__145_3_449_0
Krieger, Holly; Reschke, Paul. Cohomological Conditions on Endomorphisms of Projective Varieties. Bulletin de la Société Mathématique de France, Tome 145 (2017) no. 3, pp. 449-468. doi: 10.24033/bsmf.2744
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