1.1 Let G be a simple algebraic group over an algebraically closed field k of characteristic p > 0. For r ≥ 1, let Gr be the rth Frobenius kernel of G. It is well-known that the representations for G1 are equivalent to the restricted representations for Lie G. Historically, the cohomology for Frobenius kernels has been best understood for large primes. Friedlander and Parshall [FP] first computed the cohomology ring H(G1, k) for p ≥ 3(h− 1) where h is the Coxeter number of the underlying root system. They proved that the cohomology ring can be identified with the coordinate algebra of the nullcone. Andersen and Jantzen [AJ] later verified this fact for p ≥ h. Furthermore, they generalized this calculation by looking at H(G1,H0(λ)) where H0(λ) = indBλ for p ≥ h. Their results had some restrictions on the type of root system involved. Kumar, Lauritzen and Thomsen [KLT] removed the restrictions on the root systems through the use of Frobenius splittings. The cohomology ring H(G1, k) modulo nilpotents can be identified in general with the coordinate algebra of the restricted nullcone N1 = {x ∈ Lie(G) | x[p] = 0}. For good primes Nakano, Parshall and Vella [NPV] proved that this variety is irreducible and can be identified with the closure of some Richardson orbit. Recently, Carlson, Lin, Nakano and Parshall [CLNP] have given an explicit description of N1. These recent results provide some indication that one can systematically study extensions of Frobenius kernels for small primes by using general formulas which exhibit generic behavior for large primes.