## Nilpotent variety of restricted Lie algebra.

#### Cong Chen

In 1990, Premet conjectured that for any finite dimensional restricted Lie algebra $$L$$ over an algebraically closed field $$k$$, the nilpotent variety $$N(L)$$ is irreducible. In this talk, I will verify this conjecture for $$L=sl_{2}\otimes O_{1}+kd/dx$$, but I will start with basic theory of modular Lie algebras and state some Premet's results on $$N(L)$$.