## Kyoto Journal of Mathematics

### Algebraic cycles and Todorov surfaces

Robert Laterveer

#### Abstract

Motivated by the Bloch–Beilinson conjectures, Voisin has formulated a conjecture about $0$-cycles on self-products of surfaces of geometric genus one. We verify Voisin’s conjecture for the family of Todorov surfaces with $K^{2}=2$ and fundamental group $\mathbb{Z}/2\mathbb{Z}$. As a by-product, we prove that certain Todorov surfaces have finite-dimensional motive.

#### Article information

Source
Kyoto J. Math., Volume 58, Number 3 (2018), 493-527.

Dates
Revised: 6 July 2016
Accepted: 30 September 2016
First available in Project Euclid: 20 June 2018

https://projecteuclid.org/euclid.kjm/1529481671

Digital Object Identifier
doi:10.1215/21562261-2017-0027

Mathematical Reviews number (MathSciNet)
MR3843388

Zentralblatt MATH identifier
06959089

#### Citation

Laterveer, Robert. Algebraic cycles and Todorov surfaces. Kyoto J. Math. 58 (2018), no. 3, 493--527. doi:10.1215/21562261-2017-0027. https://projecteuclid.org/euclid.kjm/1529481671

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