THE REGULARITY THEOREM IN ALGEBRAIC GEOMETRY

(writing fij; for Qj,/c) which satisfies the usual product rule and which extends to define a structure of complex on toy ®GV M, the " absolute de Rham complex " of (M, V). Now let S be a proper and smooth C-scheme, D = u Dt a union of connected smooth divisors in S with normal crossings, such that U ^ S — D, which we will refer to as a compactification of 17. Let DerD(S/C) denote the (locally free) sheaf on S of derivations which preserve the ideal sheaf of each branch Dt of D. The sheaf of differentials on S with logarithmic singularities along D is defined by