岡潔と連接性2

[0001 １３２人目の素数さん 2023/09/15(金) 12:21:49.10 ID:9COtI6Cj]

岡潔の発見は、層ではなく連接性にあり

そして連接性とは局所有限な生成系の存在

そこにH.CartanもSerreも着目した

層が土地なら、連接性は杭

[0273 １３２人目の素数さん 2023/12/28(木) 19:52:57.81 ID:X5hzu1w5]

ハイパーコホモロジーについて何か

[0274 １３２人目の素数さん 2023/12/29(金) 06:49:02.15 ID:O2hO3W65]

早稲田で講義されたらしい

[0275 １３２人目の素数さん 2023/12/29(金) 19:01:55.00 ID:O2hO3W65]

Hypercohomology is a generalization of homology and cohomology functors in homological algebra.
It takes as input chain complexes of objects instead of objects in an abelian category.
It is a sort of cross between the derived functor cohomology of an object and
the homology of a chain complex since hypercohomology corresponds to the derived
global sections functor. The hypercohomology of a complex is calculated by
taking a quasi-isomorphism from the complex to a complex of injective elements of
an abelian category and then calculating the cohomology of the complex of
the left exact functor applied to the complex of injective elements.
Hypercohomology is used to construct cohomological long exact sequences
from arbitrary long exact sequences since its inputs are given by chain complexes
instead of just objects from an abelian category.

I hope this helps! Let me know if you have any other questions. 😊