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Zero-cycles and Brauer groups on certain Enriques surfaces
Abstract
In this paper, we study the Chow group of zero-cycles CH0(S) for certain Enriques quotients S of the Kummer surface associated to the product of two geometrically non-isogenous elliptic curves E1 and E2. We show that over fields of characteristic different from $2$ or $3$, the degree-zero subgroup A0(S) ⊂ CH0(S) is 16-torsion. Over p-adic fields, we compute the transcendental Brauer group Br(S)/Br1(S). Using the Brauer-Manin pairing, we construct examples of Enriques surfaces for which A0(S) attains nontrivial 2-torsion elements arising from push-forward from the abelian surface E1× E2.
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BibTeX
@misc{jaklitsch2026zerocycles,
title = {{Zero-cycles and Brauer groups on certain Enriques surfaces}},
author = {Thomas Jaklitsch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19307},
eprint = {2610.19307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19307},
}
RIS
TY - UNPB
TI - Zero-cycles and Brauer groups on certain Enriques surfaces
AU - Thomas Jaklitsch
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.19307
UR - https://arxiv.org/abs/2610.19307
AB - In this paper, we study the Chow group of zero-cycles CH_0(S) for certain Enriques quotients S of the Kummer surface associated to the product of two geometrically non-isogenous elliptic curves E_1 and E_2. We show that over fields of characteristic different from $2$ or $3$, the degree-zero subgroup A_0(S) ⊂ CH_0(S) is 16-torsion. Over p-adic fields, we compute the transcendental Brauer group Br(S)/Br_1(S). Using the Brauer-Manin pairing, we construct examples of Enriques surfaces for which A_0(S) attains nontrivial 2-torsion elements arising from push-forward from the abelian surface E_1× E_2.
ER -