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The singular points of $\alpha_{p}$-torsor and $\mu_{p}$-torsor of curves

Let $X$ be a smooth projective curve over an algebraically closed field of characteristic $p>0$. Suppose that the genus of $X$ is >2. Let $Y$ be a non-trivial $\alpha_{p}$-torsor or $\mu_{p}$-torsor of $X$. Write $S$ for the set of singular points of $Y$.

Is the cardinality $\sharp S>2$ ?

The singular points of $\alpha_{p}$-torsor of curves

Let $X$ be a smooth projective curve over an algebraically closed field of characteristic $p>0$. Suppose that the genus of $X$ is >2. Let $Y$ be a non-trivial $\alpha_{p}$-torsor of $X$. Write $S$ for the set of singular points of $Y$.

Is the cardinality $\sharp S>2$ ?

singular points of $\alpha_{p}$-torsor and $\mu_{p}$-torsor of curves

Let $X$ be a smooth projective curve over an algebraically closed field of characteristic $p>0$. Suppose that the genus of $X$ is >2. Let $Y$ be a non-trivial $\alpha_{p}$-torsor or $\mu_{p}$-torsor of $X$. Write $S$ for the set of singular points of $Y$.

Is the cardinality $\sharp S>2$ ?

Source Link
aya
aya
  • 187
  • 4

The singular points of $\alpha_{p}$-torsor of curves

Let $X$ be a smooth projective curve over an algebraically closed field of characteristic $p>0$. Suppose that the genus of $X$ is >2. Let $Y$ be a non-trivial $\alpha_{p}$-torsor of $X$. Write $S$ for the set of singular points of $Y$.

Is the cardinality $\sharp S>2$ ?