show · hgm.defining_parameter_ppart all knowls · up · search:

For a hypergeometric motive with defining parameters $[A, B]$ and a prime number $p$, we define the $p$-part $[A_p, B_p]$ as follows.

For each $u=a_i$ or $b_j$ in $A=(a_1,\ldots, a_m)$ and $B=(b_1,\ldots, b_n)$ we write $u=p^s v$ where $p \nmid v$. We replace $u$ with $\phi(v)$ copies of $p^s$, to get $[A', B']$, and then remove equal numbers of any overlapping elements between the multisets $A'$ and $B'$ to get $A_p$ and $B_p$.

Knowl status:
  • Review status: beta
  • Last edited by John Jones on 2017-12-01 18:36:18
Referred to by:
History: (expand/hide all)