Motives and cycles of geometrically rational varieties

（Chow-）动机理论是由上世纪最著名的数学家之一亚历山大·格罗滕狄克（Alexander Grothendieck）（1966年获得菲尔兹奖——相当于数学领域的诺贝尔奖）提出的。这是一个普遍的理论，可以解释几乎所有现有的代数对象，例如二次型、椭圆曲线或代数曲面。这些（代数）对象中的大多数在代数编码理论或密码学中起着重要作用。

The theory of (Chow-)motives has been introduced by one of the most famous mathematicians of the last century, Alexander Grothendieck (winner of the Fields medal -- the analog of the Nobel price for mathematics -- in 1966). This is an universal theory which explains almost all existing algebraic objects, as for instance quadratic forms, elliptic curves, or algebraic surfaces. Most of these (algebraic) objects play an essential role in algebraic coding theory or cryptography.