Descent of Flatness and the Direct Summand Conjecture

2016/11/13 by S. P. Dutta, Dutta, S. P.
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1611.04097

openalex publication_date 2016/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the central theorem of this article we prove the following: if R is a complete regular local ring and B is the integral closure of R in the algebraic closure of the fraction field of R, then \Hom_R(B, R) ≠ 0. Our proof of this theorem does not involve almost mathematics and it works for all characteristics. As consequences we derive the validity of a) descent of flatness for integral extensions of Noetherian rings and b) direct summand conjecture due to M. Hochster.

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