Applications of Swan's Bertini to unimodular rows

Manoj K. Keshari, Sampat Sharma

Let $R$ be an affine algebra of dimension $d\ge 4$ over a perfect field $k$ of char $\ne 2$ and $I$ be an ideal of $R$. Then - Um${}_{d+1}(R,I)/{\mathrm{E}}_{d+1}(R,I)$ has nice group s…