We show that a non-trivial fiber product S×kT of commutative noetherian local rings S,T with a common residue field k is Gorenstein if and only if it is a hypersurface of dimension 1. In this case, both S and T are regular rings of dimension 1. We also give some applications of this result.
Nasseh, Saeed, Ryo Takahashi, Keller VandeBogert.
"On Gorenstein Fiber Products and Applications."
arXIV.org Repository: 1-6.