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2019 On derived categories of arithmetic toric varieties
Matthew Ballard, Alexander Duncan, Patrick McFaddin
Ann. K-Theory 4(2): 211-242 (2019). DOI: 10.2140/akt.2019.4.211

Abstract

We begin a systematic investigation of derived categories of smooth projective toric varieties defined over an arbitrary base field. We show that, in many cases, toric varieties admit full exceptional collections, making it possible to give concrete descriptions of their derived categories. Examples include all toric surfaces, all toric Fano 3-folds, some toric Fano 4-folds, the generalized del Pezzo varieties of Voskresenskiĭ and Klyachko, and toric varieties associated to Weyl fans of type A. Our main technical tool is a completely general Galois descent result for exceptional collections of objects on (possibly nontoric) varieties over nonclosed fields.

Citation

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Matthew Ballard. Alexander Duncan. Patrick McFaddin. "On derived categories of arithmetic toric varieties." Ann. K-Theory 4 (2) 211 - 242, 2019. https://doi.org/10.2140/akt.2019.4.211

Information

Received: 13 April 2018; Revised: 3 January 2019; Accepted: 18 January 2019; Published: 2019
First available in Project Euclid: 13 August 2019

zbMATH: 07102033
MathSciNet: MR3990785
Digital Object Identifier: 10.2140/akt.2019.4.211

Subjects:
Primary: 14F05, 14M25
Secondary: 14G27, 19E08

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.4 • No. 2 • 2019
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