THE TATE CONJECTURE FOR A FAMILY OF SURFACES OF GENERAL TYPE WITH pg = q=1 AND K2=3

被引：3
|
作者：
Lyons, Christopher [1 ]
机构：
[1] Calif State Univ Fullerton, Dept Math, Fullerton, CA 92834 USA
来源：
AMERICAN JOURNAL OF MATHEMATICS | 2015年 / 137卷 / 02期
关键词：
ABELIAN-VARIETIES; WEIL CONJECTURE;
D O I：
10.1353/ajm.2015.0011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a big monodromy result for a smooth family of complex algebraic surfaces of general type, with invariants p(g) = q = 1 and K-2 = 3, that has been introduced by Catanese and Ciliberto. This is accomplished via a careful study of degenerations. As corollaries, when a surface in this family is defined over a finitely generated extension of Q, we verify the semisimplicity and Tate conjectures for the Galois representation on the middle l-adic cohomology of the surface.
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页码：281 / 311
页数：31
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