More cubic surfaces violating the Hasse principle
J\"org Jahnel
TL;DR
This paper extends Mordell's construction of cubic surfaces, demonstrating new instances where the Hasse principle does not hold, thereby providing deeper insights into rational points on cubic surfaces.
Contribution
It generalizes Mordell's method to produce more examples of cubic surfaces violating the Hasse principle.
Findings
New classes of cubic surfaces violating the Hasse principle
Extended construction techniques for such surfaces
Enhanced understanding of rational points on cubic surfaces
Abstract
We generalize L.J. Mordell's construction of cubic surfaces for which the Hasse principle fails.
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Taxonomy
TopicsMathematics and Applications · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology