TY - JOUR
AU - Podkopaev, O.
AB - The aim of this paper is to prove the following assertion: let π be a profinite group and K* be a bounded complex of discret 
$$\mathbb{F}_p[\pi]$$




F

p

[
π
]


-modules. Suppose that Hi(K*) are finite Abelian groups. Then, there exists a quasi-isomorphism L* → K*, where L* is a bounded complex of discrete 
$$\mathbb{F}_p[\pi]$$




F

p

[
π
]


-modules such that all L

i
 are finite Abelian groups. This is an analog for discrete 
$$\mathbb{F}_p[\pi]$$




F

p

[
π
]


-modules of the wellknown lemma on bounded complexes of A-modules (e.g., concentrated in nonnegative degrees), where A is a Noetherian ring, which states that any such complex is quasi-isomorphic to a complex of finitely generated A-modules, that are free with a possible exception of the module lying in degree 0. This lemma plays a key role in the proof of the base-change theorem for cohomology of coherent sheaves on Noetherian schemes, which, in turn, can be used to prove the Grothendieck theorem on the behavior of dimensions of cohomology groups of a family of vector bundles over a flat family of varieties.
TI - On One Property of Bounded Complexes of Discrete $$\mathbb{F}_p[\pi]$$ -modules
JO - Vestnik St. Petersburg University: Mathematics
DO - 10.3103/S1063454118040131
DA - 2019-02-06
UR - https://www.deepdyve.com/lp/springer-journals/on-one-property-of-bounded-complexes-of-discrete-mathbb-f-p-pi-modules-Ihl1XTaayJ
SP - 386
EP - 390
VL - 51
IS - 4
DP - DeepDyve
ER -