|
|||||
 |
|
|
|
|
|
|
|
On a cohomological
generalization of the Shafarevich conjecture for K3
surfaces
Teppei Takamatsu |
|
Vol. 14 (2020), No. 9, 2505–2531
|
Abstract |
|
The Shafarevich conjecture for K3 surfaces asserts the finiteness of isomorphism classes of K3 surfaces over a fixed number field admitting good reduction away from a fixed finite set of finite places. André proved this conjecture for polarized K3 surfaces of fixed degree, and recently She proved it for polarized K3 surfaces of unspecified degree. We prove a certain generalization of their results, which is stated by the unramifiedness of -adic étale cohomology groups for K3 surfaces over finitely generated fields of characteristic . As a corollary, we get the original Shafarevich conjecture for K3 surfaces without assuming the extendability of polarization, which is stronger than the results of André and She. Moreover, as an application, we get the finiteness of twists of K3 surfaces via a finite extension of characteristic fields. |
PDF Access Denied
We have not been able to recognize your IP address
3.17.110.162
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
K3 surfaces, Shafarevich conjecture, good reduction
|
Mathematical Subject Classification 2010
Primary: 14J28
Secondary: 11F80, 11G18, 11G25, 11G35
|
Milestones
Received: 15 October 2019
Revised: 11 March 2020
Accepted: 11 May 2020
Published: 13 October 2020
|
Authors |
| Teppei Takamatsu | |
| Graduate School of Mathematical
Sciences The University of Tokyo Tokyo Japan |
|
