The Semicontinuity theorem


莊家華 ( National Taiwan University )
2022-08-30  14:00 - 16:00
Room 201, Astronomy and Mathematics Building

We have studied the local constancy of Euler characteristics of flat sheaves in a family of projective schemes parametrized by noetherian base, in this section we will continue the study of the variation of fibral cohomologies and prove the semicontinuity theorem.
The equivalence of the pointwise completion of higher direct images and the limit of cohomologies taken in the “infinitesimal neighborhoods” of arbitrary order of the corresponding fiber has also been established, we will apply the result to prove the theorem relates the fibral cohomologies and the corresponding base changes of higher direct images.