title: Arithmetic variety
text: # Arithmetic variety
  
  In mathematics, an arithmetic variety is the quotient space of a Hermitian symmetric space by an arithmetic subgroup of the associated algebraic Lie group.
  
  ## Kazhdan's theorem
  
  Kazhdan's theorem says the following:
  
  Kazhdan's theorem — If X is an arithmetic variety, then, for all automorphisms σ of the complex numbers, σX is also an arithmetic variety.
  
  