Hyperdescent and \'etale K-theory

We study the 'etale sheafification of algebraic K-theory, called 'etale K-theory. Our main results show that 'etale 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 'etale 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 'etale sites.