Local cohomology of module of differentials of integral extensions

S. P. Dutta

doi:10.1016/j.jalgebra.2021.04.023

Local cohomology of module of differentials of integral extensions

S. P. Dutta

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The main focus of this paper is on determining the highest non-vanishing local cohomology modules of Ω_B/R,Ω_B/V(Ω_B/k) where R is either a complete regular local ring or a complete local normal domain with coefficient ring V (field k) and B is its integral closure in an algebraic extension of Q(R). Similar problem is also studied over a normal domain R containing a field k of characteristic 0. In this connection new observations on the direct summand property for integral extensions are also presented.

Original language	English (US)
Pages (from-to)	136-156
Number of pages	21
Journal	Journal of Algebra
Volume	582
DOIs	https://doi.org/10.1016/j.jalgebra.2021.04.023
State	Published - Sep 15 2021

Keywords

Formally unramified extensions
Geometric regularity
Integral extension
Local cohomology
Module of differentials

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1016/j.jalgebra.2021.04.023

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abstract = "The main focus of this paper is on determining the highest non-vanishing local cohomology modules of ΩB/R,ΩB/V(ΩB/k) where R is either a complete regular local ring or a complete local normal domain with coefficient ring V (field k) and B is its integral closure in an algebraic extension of Q(R). Similar problem is also studied over a normal domain R containing a field k of characteristic 0. In this connection new observations on the direct summand property for integral extensions are also presented.",

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AB - The main focus of this paper is on determining the highest non-vanishing local cohomology modules of ΩB/R,ΩB/V(ΩB/k) where R is either a complete regular local ring or a complete local normal domain with coefficient ring V (field k) and B is its integral closure in an algebraic extension of Q(R). Similar problem is also studied over a normal domain R containing a field k of characteristic 0. In this connection new observations on the direct summand property for integral extensions are also presented.

KW - Formally unramified extensions

KW - Geometric regularity

KW - Integral extension

KW - Local cohomology

KW - Module of differentials

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VL - 582

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EP - 156

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Local cohomology of module of differentials of integral extensions

Abstract

Keywords

ASJC Scopus subject areas

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