Indecomposable polynomials and their spectrum
  We address some questions concerning indecomposable polynomials and their spectrum. How does the spectrum behave via reduction or specialization, or via a more general ring morphism? Are the indecomposability properties equivalent over a field and over its algebraic closure? How many polynomials are decomposable over a finite field? 
Arnaud Bodin, Pierre D\`ebes, Salah Najib