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Fields of characteristic $p$, i.e., fields for which there is a prime $p$ such that $px=0$ for each $x$. Do not use this tag for questions on characteristic polynomials of a matrix.
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A short proof for simple connectedness of the projective line
You can apply the following statement to $X = \mathbb{P}^1_K$ and $L = O(1)$ when $K$ is a separably closed field.
Let $L$ be a line bundle on a reduced connected scheme $X$ such that $H^{0}( …