scholarly journals Rational Points on K3 Surfaces and Derived Equivalence

2017 ◽  
pp. 87-113 ◽  
Author(s):  
Brendan Hassett ◽  
Yuri Tschinkel
Keyword(s):  
K3 Surfaces ◽  
Rational Points ◽  
Derived Equivalence

scholarly journals K3 surfaces, rational curves, and rational points

2010 ◽  
Vol 130 (7) ◽  
pp. 1470-1479 ◽  
Author(s):  
Arthur Baragar ◽  
David McKinnon
Keyword(s):  
K3 Surfaces ◽  
Rational Points ◽  
Rational Curves

scholarly journals Density of rational points on elliptic K3 surfaces

2000 ◽  
Vol 4 (2) ◽  
pp. 351-368 ◽  
Author(s):  
F. A. Bogomolov ◽  
Yu. Tschinkel
Keyword(s):  
K3 Surfaces ◽  
Rational Points

scholarly journals Non-Euclidean pythagorean triples, a problem of euler, and rational points on K3 surfaces

2008 ◽  
Vol 30 (4) ◽  
pp. 4-10 ◽  
Author(s):  
Robin Hartshorne ◽  
Ronald Van Luijk
Keyword(s):  
K3 Surfaces ◽  
Rational Points ◽  
Pythagorean Triples

scholarly journals Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties

2020 ◽  
Vol 26 (3) ◽  
Author(s):  
Atsushi Ito ◽  
Makoto Miura ◽  
Shinnosuke Okawa ◽  
Kazushi Ueda
Keyword(s):  
Abelian Varieties ◽  
K3 Surfaces ◽  
Derived Equivalence ◽  
Grothendieck Ring

Rational points on K3 surfaces in ?1 � ?1 � ?1

1996 ◽  
Vol 305 (1) ◽  
pp. 541-558 ◽  
Author(s):  
A. Baragar
Keyword(s):  
K3 Surfaces ◽  
Rational Points

scholarly journals Rational points and derived equivalence

2021 ◽  
Vol 157 (5) ◽  
pp. 1036-1050
Author(s):  
Nicolas Addington ◽  
Benjamin Antieau ◽  
Katrina Honigs ◽  
Sarah Frei
Keyword(s):  
Rational Point ◽  
Source Code ◽  
Rational Points ◽  
The Other ◽  
Online Version ◽  
Hasse Principle ◽  
Derived Equivalence ◽  
Derived Equivalences ◽  
Closed Fields ◽  
Supplementary Material

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 $\mathbb {Q}$ and $\mathbb {F}_q(t)$ , and conclude with a pair of hyperkähler 4-folds over $\mathbb {Q}$ . 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.

scholarly journals Rational Points on Twisted K3 Surfaces and Derived Equivalences

2017 ◽  
pp. 13-28 ◽  
Author(s):  
Kenneth Ascher ◽  
Krishna Dasaratha ◽  
Alexander Perry ◽  
Rong Zhou
Keyword(s):  
K3 Surfaces ◽  
Rational Points ◽  
Derived Equivalences

scholarly journals Rational points on elliptic K3 surfaces of quadratic twist type

2020 ◽  
Author(s):  
Zhizhong Huang
Keyword(s):  
Elliptic Curves ◽  
K3 Surfaces ◽  
Rational Points ◽  
Zariski Topology ◽  
Quadratic Twists ◽  
Quadratic Twist ◽  
Quartic Polynomials

Abstract In studying rational points on elliptic K3 surfaces of the form $$\begin{equation*} f(t)y^2=g(x), \end{equation*}$$ where f, g are cubic or quartic polynomials (without repeated roots), we introduce a condition on the quadratic twists of two elliptic curves having simultaneously positive Mordell–Weil rank, and we relate it to the Hilbert property. Applying to surfaces of Cassels–Schinzel type, we prove unconditionally that rational points are dense both in Zariski topology and in real topology.

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