Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userChow Groups of Quadrics in Characteristic Two
132
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Let $X$ be a smooth projective quadric defined over a field of characteristic 2. We prove that in the Chow group of codimension 2 or 3 of $X$ the torsion subgroup has at most two elements. In codimension 2, we determine precisely when this torsion subgroup is nontrivial. In codimension 3, we show that there is no torsion if {$dim Xge 11$.} This extends the analogous results in characteristic different from 2, obtained by Karpenko in the nineteen-nineties.
rate research
Read More
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.
We prove that a smooth complete intersection of two quadrics of dimension at least $2$ over a number field has index dividing $2$, i.e., that it possesses a rational $0$-cycle of degree $2$.
In these lectures, we provide a toolkit to work with Chow-Witt groups, and more generally with the homology and cohomology of the Rost-Schmid complex associated to Milnor-Witt $K$-theory.
We determine the Chow rings of the complex algebraic groups of the exceptional type E_6, E_7, and E_8, giving the explicit generators represented by the pull-back images of Schubert varieties of the corresponding flag varieties. This is a continuation of the work of R. Marlin on the computation of the Chow rings of SO_n, Spin_n, G_2, and F_4. Our method is based on Schubert calculus of the corresponding flag varieties, which has its own interest.
We describe examples motivated by the work of Serre and Abhyankar.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
