On the Picard number of K3 surfaces over number fields

被引：28
|
作者：
Charles, Francois [1 ]
机构：
[1] Univ Rennes 1, Inst Rech Math Rennes, F-35042 Rennes, France
来源：
ALGEBRA & NUMBER THEORY | 2014年 / 8卷 / 01期
关键词：
K3; surfaces; Picard number; Neron-Severi group; MUMFORD-TATE CONJECTURE; VARIETIES; MONODROMY;
D O I：
10.2140/ant.2014.8.1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We discuss some aspects of the behavior of specialization at a finite place of Neron-Severi groups of K3 surfaces over number fields. We give optimal lower bounds for the Picard number of such specializations, thus answering a question of Elsenhans and Jahnel. As a consequence of these results, we show that it is possible to compute explicitly the Picard number of any given K3 surface over a number field.
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收藏
页码：1 / 17
页数：17
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