Degree as a monoid. (English) Zbl 1485.14043

Bedi, Harpreet Singh

Rocky Mt. J. Math. 51, No. 5, 1521-1539 (2021).

Summary: “Polynomials” with degree as an ordered monoid say \(\Delta\) are constructed along with corresponding schemes and line bundles \(\mathcal{O}(d)\), \(d \in \Delta\). The cohomology of these line bundles is then computed using Čech complex and new proof of zero cohomology of affine schemes is given. The last section of the paper applies the theory developed for the construction and computation of affine cohomology of perfectoid Tate algebras.

MSC:

14G45	Perfectoid spaces and mixed characteristic
14A15	Schemes and morphisms
14F06	Sheaves in algebraic geometry

Keywords:

degree; line bundles; perfectoid; Čech cohomology

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