<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>X</italic> be projective variety over an algebraically closed field <italic>k</italic> and <italic>G</italic> be a finite group with <italic>g.c.d.</italic>(<italic>char</italic>(<italic>k</italic>), |<italic>G</italic>|) = 1. We prove that any representations of <italic>G</italic> on a coherent sheaf, <italic>ρ</italic> : <italic>G</italic> → <italic>End</italic>(ℰ), has a natural decomposition ℰ ≃ ⊕ <italic>V</italic> ⊗<italic>k</italic> ℱ<italic>V</italic>, where <italic>G</italic> acts trivially on ℱ<italic>V</italic> and the sum run over all irreducible representations of <italic>G</italic> over <italic>k</italic>.</abstract>

Let X be projective variety over an algebraically closed field k and G be a finite group with g.c.d.(char(k), |G|) = 1. We prove that any representations of G on a coherent sheaf, ρ : G → End(ℰ), has a natural decomposition ℰ ≃ ⊕ V ⊗k ℱV, where G acts trivially on ℱV and the sum run over all irreducible representations of G over k.

A Krull-Schmdit type theorem for coherent sheaves

Department of Mathematics, Universida Autónoma ”Benito Juárez” de Oaxaca, Av Universidad s/n Oaxaca de Juárez, México.

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A Krull-Schmdit type theorem for coherent sheaves"}

Let X be projective variety over an algebraically closed field k and G be a finite group with g.c.d.(char(k), |G|) = 1. We prove that any representations of G...

A Krull-Schmdit type theorem for coherent sheaves

Published Online: Oct 20, 2015

Page range: 51 - 56

Received: Apr 01, 2012

Accepted: Feb 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0030

Keywords
Group representations on sheaves, Krull-Schmdit theorem, projective varieties

© 2014 A. S. Argáez, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Krull-Schmdit type theorem for coherent sheaves

Published Online: Oct 20, 2015

Page range: 51 - 56

Received: Apr 01, 2012

Accepted: Feb 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0030

KeywordsGroup representations on sheaves, Krull-Schmdit theorem, projective varieties

© 2014 A. S. Argáez, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Group representations on sheaves, Krull-Schmdit theorem, projective varieties