Unramified Cohomology of Quadrics in Characteristic Two

Abstract

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.

Final verstion, to appear in Manuscripta Mathematica

References in corpus (3)

• Revêtements étales et groupe fondamental (SGA 1)
• Chow Groups of Quadrics in Characteristic Two
• Unramified Cohomology of Quadrics in Characteristic Two

Cited by in corpus (2)

• Chow Groups of Quadrics in Characteristic Two
• Unramified Cohomology of Quadrics in Characteristic Two