COUNTEREXAMPLES TO THE HASSE PRINCIPLE IN FAMILIES

2021 ◽  
pp. 1-10
Author(s):  
NGUYEN XUAN THO
Keyword(s):  
Hasse Principle ◽  
Quartic Surfaces

Abstract We generalise two quartic surfaces studied by Swinnerton-Dyer to give two infinite families of diagonal quartic surfaces which violate the Hasse principle. Standard calculations of Brauer–Manin obstructions are exhibited.

scholarly journals On the Brauer group of diagonal quartic surfaces

2011 ◽  
Vol 83 (3) ◽  
pp. 659-672 ◽  
Author(s):  
Evis Ieronymou ◽  
Alexei N. Skorobogatov ◽  
Yuri G. Zarhin
Keyword(s):  
Brauer Group ◽  
Quartic Surfaces

Thue equations that simultaneously fail the Hasse principle

2021 ◽  
pp. 1-10
Author(s):  
PALOMA BENGOECHEA
Keyword(s):  
Positive Integer ◽  
Hasse Principle ◽  
Fixed Degree ◽  
Binary Forms ◽  
Absolute Value ◽  
Positive Proportion ◽  
The Absolute

Abstract We refine a previous construction by Akhtari and Bhargava so that, for every positive integer m, we obtain a positive proportion of Thue equations F(x, y) = h that fail the integral Hasse principle simultaneously for every positive integer h less than m. The binary forms F have fixed degree ≥ 3 and are ordered by the absolute value of the maximum of the coefficients.

On the Hasse principle for cubic surfaces

Mathematika ◽  
1966 ◽  
Vol 13 (2) ◽  
pp. 111-120 ◽  
Author(s):  
J. W. S. Cassels ◽  
M. J. T. Guy
Keyword(s):  
Hasse Principle ◽  
Cubic Surfaces
Sign in / Sign up

Export Citation Format

Share Document