Some homological properties of $GL(m|n)$ in arbitrary characteristic

We show that Penkov's approach to a superanalog of Borel-Bott-Weil theorem for $G=GL(m|n)$ over a field of zero characteristic can be extended for a perfect field of arbitrary odd characteristic. We also prove some partial version of Kempf's vanishing theorem and characteristic free formula for Euler characteristic $χ(B, λ^ε)$, where $B$ is a Borel subgroup of $G$.

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