Potentially stably rational conic bundle

This page contains Magma code to compute $H^1(G,Pic(\bar{X}))$ where $X$ is a standard conic bundle and $G$ is the Galois group of the splitting field of $X$,the splitting group $G$ is a subgroup of Weyl group of root system $D_n$, $W(D_n)$.

Magma code:

• Computes cohomology obstruction $H^1(G,Pic(\bar{X}))$.

We view $W(D_n) \subset W(D_9)$ for $i=4,5,6,7,8$ and give them 11-dimension representations.

Results:

• Instructions and examples
• Subgroup of $W(D_4)$
• Subgroup of $W(D_5)$
• Subgroup of $W(D_6)$
• Subgroup of $W(D_7)$
• Subgroup of $W(D_8)$
• Subgroup of $W(D_9)$