On nilpotent commuting varieties and cohomology of Frobenius kernels
  The paper studies the dimensions of irreducible components of commuting varieties of (restricted) nilpotent $r$-tuples in a classical Lie algebra $\mathfrak{g}$ defined over an algebraically closed field $k$. As applications, we obtain some new results on the structure of the (even) cohomology ring of Frobenius kernels $G_r$ for each $r\ge 1$, where $G$ is the simply connected, simple algebraic group such that $\text{Lie}(G)=\mathfrak{g}$. Explicit calculations for rank two groups are also presented. 
Nham V. Ngo
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