Let $X$ be an algebraic stack of finite type over a field.


Is there an intrinsic way to calculate the minimum of the dimensions of all atlases of $X$?


By intrinsic here I mean using constructions such as the inertia stack, the stabilizer group construction, etc.


A natural conjecture is that this minimum should be something like the dimension of $X$ plus the dimension of the largest stabilizer of any point of $X$, as one can see using classifying stacks, for example.



Smallest atlas for algebraic stack
Professor Jarod Alper provided me an answer to this question in separate correspondence. When the stabilizer at a point of the stack is smooth, my conjecture above is true by the theory of miniversal deformations. This is Theorem 3.6.1 in Professor Alper's notes here: [https://sites.math.washington.edu/~jarod/moduli.pdf](https://sites.math.washington.edu/%7Ejarod/moduli.pdf).


