Abstract
Let k be an algebraically closed field of arbitrary characteristic. We give a self-contained algebraic proof of the following statement: If V is an affine surface over k such that V × k ≅ k 3 , then V ≅ k 2 . This fact, which is due to Fujita, Miyanishi, Sugie, and Russell, solves the Zariski cancellation problem for surfaces. To achieve our proof, we first show that if A is a finitely generated domain with AK ( A ) = A , then AK ( A [ x ] ) = A .
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