Given a coherent sheaf F over a noetherian scheme Y, a classical result in algebraic geometry states the upper-semocontinuity of the function sending any point $y \in Y$ to $\mathrm{dim}_{k(y)}(F \otimes k(y))$.

What about similar results for the length function, i.e. $\mathrm{lt}_{O_y}(F_y)$?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.