Smoothness is the same as regularity at closed points for a finite type scheme of pure dimension $d$ over an algebraically closed field
71296
Problem with Jacobian criterion and regular local ring
131000
A proof of a criterion of vanishing of a function.
148203
The genus of an algebraic curve is invariant under isomorphisms
32910
Completion and algebraic closure commutable
99707
free module implies surjective map of affine schemes
57283
Extending Homomorphism into Algebraically Closed Field
145039
Algebraic independence over $\overline{\mathbb Q}$ and over $\mathbb Q$
33969
"Basis extension theorem" for local smooth vector fields
100340
Invariant dimension property on a ring without zero divisors
97669
Sheafs and closed immersion
122050
Algebraic extension of perfect field in which every polynomial has a root is algebraically closed
145820
Mumford's regularity theorem
92677
Infinite algebraic extension of a finite field
46504
Does there exist a smooth approximation of $x \bmod y$?
113136
Generators of the ideal correspond to $d$-uple embedding
107370
An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
58562
How can we prove that $D(f)\backsimeq\operatorname{Spec} A_f$?