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Post Reopened by Joel David Hamkins, Simon Henry, Leo Alonso, Neil Strickland, Stefan Kohl

Let A$A$ be an integral complete local ring over a field which is complete intersection.

Let B$B$ be a normalization of A$A$.

Q. Is B gorenstein$B$ Gorenstein?

I guess that even the normalization of gorensteinGorenstein local ring should be gorensteinGorenstein.

Let A be an integral complete local ring over a field which is complete intersection.

Let B be a normalization of A.

Q. Is B gorenstein?

I guess that even the normalization of gorenstein local ring should be gorenstein.

Let $A$ be an integral complete local ring over a field which is complete intersection.

Let $B$ be a normalization of $A$.

Q. Is $B$ Gorenstein?

I guess that even the normalization of Gorenstein local ring should be Gorenstein.

Post Closed as "Not suitable for this site" by abx, Wolfgang, Alex Degtyarev, Daniel Loughran, Olivier
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Normalization of complete intersection

Let A be an integral complete local ring over a field which is complete intersection.

Let B be a normalization of A.

Q. Is B gorenstein?

I guess that even the normalization of gorenstein local ring should be gorenstein.