The Library
Finiteness theorems for K3 surfaces and abelian varieties of CM type
Tools
Orr, Martin and Skorobogatov, Alexei N. (2018) Finiteness theorems for K3 surfaces and abelian varieties of CM type. Compositio Mathematica, 154 (08). pp. 1571-1592. doi:10.1112/S0010437X18007169 ISSN 0010-437X.
An open access version can be found in:
Official URL: http://dx.doi.org/10.1112/S0010437X18007169
Abstract
We study abelian varieties and K3 surfaces with complex multiplication defined over number fields of fixed degree. We show that these varieties fall into finitely many isomorphism classes over an algebraic closure of the field of rational numbers. As an application we confirm finiteness conjectures of Shafarevich and Coleman in the CM case. In addition we prove the uniform boundedness of the Galois invariant subgroup of the geometric Brauer group for forms of a smooth projective variety satisfying the integral Mumford–Tate conjecture. When applied to K3 surfaces, this affirms a conjecture of Várilly-Alvarado in the CM case.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Compositio Mathematica | ||||||||
Publisher: | Cambridge University Press | ||||||||
ISSN: | 0010-437X | ||||||||
Official Date: | August 2018 | ||||||||
Dates: |
|
||||||||
Volume: | 154 | ||||||||
Number: | 08 | ||||||||
Page Range: | pp. 1571-1592 | ||||||||
DOI: | 10.1112/S0010437X18007169 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Related URLs: | |||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |