Hongdi Huang, Department of Pure Mathematics, University of Waterloo
"The Zariski Cancellation Problem"
Let k be an algebraically closed field. The classical Zariski Cancellation Problem for Affine Spaces asks whether the affine space An is cancellative: if V is an affine k -variety such that V × A1 ∼= An+1∼nk kk, does it follow that V = Ak? Equivalently, if A is an affine k -algebra such that A[X] is isomorphicto the polynomial ring k[X1,...,Xn+1], does it follow that A is isomorphic to k[X1,...,Xn]? Ring theoretically, one can ask more generally for R some specific algebras, when does R[t] ∼= S[t] imply that R and S are isomorphic as algebras? In this talk, we will introduce some useful tools to approach this problem and some known results by far.
MC 5403