Towards a homological generalization of the direct summand theorem-Reference-Cited by-同舟云学术

Towards a homological generalization of the direct summand theorem

Published:2020-01-01 Issue:1 Volume:18 Page:1352-1364
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Vélez-Caicedo Juan Diego¹,Gómez-Ramírez Danny Arlen de Jesús²

Affiliation:

1. Universidad Nacional de Colombia, Escuela de Matemáticas , Calle 59A No 63 - 20, Núcleo El Volador , Medellín , Colombia

2. Instituto Tecnológico Metropolitano (ITM) Cl. 54a # 30-01, Medellín, Colombia and Cognivisión S. A. S. , Itagüi , Colombia

Abstract

Abstract We present a more general homological characterization of the direct summand theorem (DST). Specifically, we state two new conjectures: the socle-parameter conjecture (SPC) in its weak and strong forms. We give a proof for the weak form by showing that it is equivalent to the DST. Furthermore, we prove the SPC in its strong form for the case when the multiplicity of the parameters is smaller than or equal to two. Finally, we present a new proof of the DST in the equicharacteristic case, based on the techniques thus developed.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0087/pdf

Reference26 articles.

1. M. Hochster, Homological conjectures, old and new, Illinois J. Math. 51 (2007), 151–159.

2. C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale, I.H.E.S. Publ. Math. 42 (1973), 323–395.

3. J.-P. Serre, Local Algebra, Springer Science & Business Media, Berlin Heidelberg, 2012.

4. M. Hochster, The direct summand conjecture and canonical elements in local cohomology modules, J. Algebra 84 (1983), 503–553.

5. T. Ohi, Direct summand conjecture and descent for flatness, Proc. Am. Math. Soc. 124 (1996), no. 7, 1967–1968.