Descent of Flatness and the Direct Summand Conjecture

S. P. Dutta

Descent of Flatness and the Direct Summand Conjecture

Commutative Algebra 2016-11-18 v2

Authors: S. P. Dutta

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 $\Hom_R(B, R) \neq 0$ . 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.

Keywords

descent of flatness direct summand conjecture complete regular local ring integral closure Noetherian rings almost mathematics algebraic closure

Cite

@article{arxiv.1611.04097,
  title  = {Descent of Flatness and the Direct Summand Conjecture},
  author = {S. P. Dutta},
  journal= {arXiv preprint arXiv:1611.04097},
  year   = {2016}
}

Comments

This paper has been withdrawn by the author due to a gap in the proof of the main theorem

Descent of Flatness and the Direct Summand Conjecture

Abstract

Keywords

Cite

Comments

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