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Unramified Cohomology of Quadrics in Characteristic Two

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 Added by Yong Hu
 Publication date 2021
  fields
and research's language is English




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Let $F$ be a field of characteristic 2 and let $X$ be a smooth projective quadric of dimension $ge 1$ over $F$. We study the unramified cohomology groups with 2-primary torsion coefficients of $X$ in degrees 2 and 3. We determine completely the kernel and the cokernel of the natural map from the cohomology of $F$ to the unramified cohomology of $X$. This extends the results in characteristic different from 2 obtained by Kahn, Rost and Sujatha in the nineteen-nineties.



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