On the arithmetic of intersections of two quadrics containing a conic
Per Salberger
TL;DR
This paper proves two conjectures related to the arithmetic of intersections of two quadrics that contain a conic, providing new insights into their structure and properties.
Contribution
It offers the first proofs of two longstanding conjectures concerning the arithmetic of such intersections in the presence of a conic.
Findings
Proofs of two conjectures by Colliot-Thélène, Sansuc, and Swinnerton-Dyer.
Enhanced understanding of the arithmetic of intersections of quadrics containing a conic.
Contributions to the theory of rational points on algebraic varieties.
Abstract
This is a retyped version of an unpublished manuscript from 1993. It contains proofs of two conjectures of Colliot-Th\'el\`ene, Sansuc and Swinnerton-Dyer on the arithmetic of intersections of two quadrics in the case where the variety contains a conic.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques · Polynomial and algebraic computation