Frobenius morphisms and derived categories on two dimensional toric Deligne-Mumford stacks

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Abstract

For a toric Deligne-Mumford (DM) stack X, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism F:X→X on a dimensional toric DM stack X, we show that the push-forward F*OX of the structure sheaf generates the bounded derived category of coherent sheaves on X .We also choose a full strong exceptional collection from the set of direct summands of F *OX in several examples of two dimensional toric DM orbifolds X. © 2013 Elsevier Ltd.

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Ohkawa, R., & Uehara, H. (2013). Frobenius morphisms and derived categories on two dimensional toric Deligne-Mumford stacks. Advances in Mathematics, 244, 241–267. https://doi.org/10.1016/j.aim.2013.04.023

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