Conics - a Poor Man's Elliptic Curves

关于含一条圆锥曲线的两个二次曲面交的算术

On the arithmetic of intersections of two quadrics containing a conic

本文重录1993年未发表手稿，证明了Colliot-Thélène、Sansuc与Swinnerton-Dyer关于含圆锥曲线的两个二次曲面交算术性质的两个猜想。

Quadratic families of elliptic curves and unirationality of degree 1 conic bundles

We consider elliptic curves whose coefficients are degree 2 polynomials in a variable t. We prove that for infinitely many values of t the resulting elliptic curve has rank at least 1. All such curves together form an algebraic surface which is birational to a conic bundle with 7 singular fibers. The main step of the proof is to show that such conic bundles are unirational. V.2: Main theorem is corrected for small finite fields.

在有理椭圆面中通过构造圆锥实现适度的秩跳跃

Moderate rank jumps on rational elliptic surfaces via construction of conics

本文通过构造圆锥方法，在有理椭圆面中实现秩的适度跳跃，研究具有高秩纤维的椭圆面家族。