Grothendieck--Lefschetz type theorems for the local Picard group
  We propose a strengthening of the Grothendieck--Lefschetz hyperplane theorem for the local Picard group, prove some special cases and derive several consequences to the deformation theory of log canonical singularities. Version 2: Main conjecture changed, following recent results of Bhatt and de Jong. Small changes to the proofs. 
J\'anos Koll\'ar (Princeton Univ)
math.AG