We study the étale sheafification of algebraic K-theory, called étale K-theory. Our main results show that étale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is defined at the level of categories. Consequently, we show that étale K-theory has surprisingly well-behaved properties, integrally and without finiteness assumptions. A key theoretical ingredient is the distinction, which we investigate in detail, between sheaves and hypersheaves of spectra on étale sites.

中文翻译：

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超血统和étaleK理论

我们研究代数的étalesheafification ķ -理论，叫做étale ķ -理论。我们的主要结果表明，étale ķ -理论非常接近，称之为塞尔默一个非交换不变ķ -理论，这是在类的级别定义。因此，我们表明，étale ķ -理论具有令人惊讶的乖巧性，整体和无有限性假设。理论上的关键要素是区别，我们将详细研究étale站点的频谱的滑轮和超滑轮之间的区别。