## Annals of K-Theory

### On derived categories of arithmetic toric varieties

#### 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.

#### Article information

Source
Ann. K-Theory, Volume 4, Number 2 (2019), 211-242.

Dates
Revised: 3 January 2019
Accepted: 18 January 2019
First available in Project Euclid: 13 August 2019

https://projecteuclid.org/euclid.akt/1565661792

Digital Object Identifier
doi:10.2140/akt.2019.4.211

Mathematical Reviews number (MathSciNet)
MR3990785

Zentralblatt MATH identifier
07102033

#### Citation

Ballard, Matthew; Duncan, Alexander; McFaddin, Patrick. On derived categories of arithmetic toric varieties. Ann. K-Theory 4 (2019), no. 2, 211--242. doi:10.2140/akt.2019.4.211. https://projecteuclid.org/euclid.akt/1565661792

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