Rational points and derived equivalence

被引：4

作者：

Addington, Nicolas ^{[1
]}

Antieau, Benjamin ^{[2
]}

Honigs, Katrina ^{[1
]}

Frei, Sarah ^{[3
]}

机构：

[1] Univ Oregon, Dept Math, Eugene, OR 97403 USA

[2] Northwestern Univ, Dept Math, 2033 Sheridan Rd, Evanston, IL 60208 USA

[3] Rice Univ, Dept Math, 6100 Main St, Houston, TX 77005 USA

来源：

COMPOSITIO MATHEMATICA | 2021年 / 157卷 / 05期

关键词：

derived categories of coherent sheaves; rational points; Brauer-Manin obstructions; moduli spaces of sheaves; K3; surfaces; holomorphic symplectic varieties; HASSE PRINCIPLE; K3; SURFACES; SHEAVES; CURVES; MODULI; CATEGORIES; VARIETIES; DUALITY;

D O I：

10.1112/S0010437X21007089

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give the first examples of derived equivalences between varieties defined over non-closed fields where one has a rational point and the other does not. We begin with torsors over Jacobians of curves over Q and F-q(t), and conclude with a pair of hyperkahler 4-folds over Q. The latter is independently interesting as a new example of a transcendental Brauer-Manin obstruction to the Hasse principle. The source code for the various computations is supplied as supplementary material with the online version of this article.

引用

页码：1036 / 1050

页数：15

共 32 条

[1] Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences [J].