Asset Details
Do you wish to reserve the book?
An O-acyclic variety of even index
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
An O-acyclic variety of even index
Do you wish to request the book?
An O-acyclic variety of even index
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
An O-acyclic variety of even index
2024
Overview
We give the first examples of O-acyclic smooth projective geometrically connected varieties over the function field of a complex curve, whose index is not equal to one. More precisely, we construct a family of Enriques surfaces over P1 such that any multi-section has even degree over the base P1 and show moreover that we can find such a family defined over Q. This answers affirmatively a question of Colliot-Thélène and Voisin. Furthermore, our construction provides counterexamples to: the failure of the Hasse principle accounted for by the reciprocity obstruction; the integral Hodge conjecture; and universality of Abel–Jacobi maps.
Publisher
Springer Nature B.V
Subject
