Lectures on Formal and Rigid Geometry by Siegfried Bosch

Author:Siegfried Bosch
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

where the limit runs over all admissible coverings of X, is called the qth Čech cohomology group of X with values in . There is always a canonical morphism

that it is bijective for q = 0, 1 and injective for q = 2. To compute higher cohomology groups via Čech cohomology, one needs special assumptions.

Theorem 5.

Let be an admissible covering of a rigid K-space X and let be an -module. Assume for q > 0 and U any finite intersection of sets in . Then the canonical map

is bijective for all q ≥ 0.

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