Bass conjecture

In mathematics, especially algebraic geometry, the Bass conjecture says that certain algebraic K-groups are supposed to be finitely generated.

Any of the following equivalent statements is referred to as the Bass conjecture.

The equivalence of these statements follows from the agreement of K- and K'-theory for regular rings and the localization sequence for K'-theory.

Daniel Quillen showed that the Bass conjecture holds for all (regular, depending on the version of the conjecture) rings or schemes of dimension ≤ 1, i.e., algebraic curves over finite fields and the spectrum of the ring of integers in a number field.

The (non-regular) ring A = Z[x, y]/x2 has an infinitely generated K1(A).