Krdytkyu

0 $begingroup$ I know that in general, the stalks of the pushforward of a sheaf need not be the same as the original stalk. That is, $(f_{*}mathcal{F})_{f(p)}=mathcal{F}_p$ is not true in general. But when $X subset Y$ and $f$ is the inclusion map, is it true that the above holds for $p in X$ and that the stalks are zero(or the terminal object) for points not in X? I am asking this because I was able to prove this for any subset, but in Hartshorne Chapter 2, exercise 19, he asks you to prove that this holds for closed subsets and that a different construction(denoted $f_{!}mathcal{F}$ ) gives these stalks for open subsets. algebraic-geometry sheaf-theory share | cite | improve this question

1 1 $begingroup$ I am learning to solve cubic equation by cardano's method from here and what are saying only gives one root I can't seem to work these equations Q1 $x^3-15x=126$ , Q2. $x^3+3x^2+21x+38=0$ so any other question some give only one root other start to give imaginary answer just how can i calculate that? any suggestion or book reference would be nice. Also are there different types of equation in Cardano's method polynomials cubic-equations share | cite | improve this question edited Dec 22 '18 at 9:36 Sik Feng Cheong 157 9