# Are non-maximal orders in number fields Grothendieck rings?

Recall that a ring homomorphism A->B is geometrically regular if for all primes p of A, the fiber of B over p is geometrically regular over k(p). A Grothendieck ring (or, G-ring) is one for which A_p->A_p* is regular for all primes p. These are the maps from the local rings of A to their completions.

If A is an order in a number field, is A a G-ring? Equivalently (in this special case), is A excellent?

I've heard it said that 'all' rings that appear in algebraic geometry are excellent. Since an order A corresponds to a singular curve, I guess I expect A to be excellent as well.

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