# This Collection

By Defense Date By Authors By Titles By Subject

# Statistics

View Statistics All RECERCAT

# My RECERCAT

Login E-mail Alerts

To access the full text documents, please follow this link: http://hdl.handle.net/2117/1201

 Title: Vanishing of the André-Quillen homology Module$H$2(A,B,G (I)) Planas Vilanova, Francesc d'Assís Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions Let $I$ be an ideal of a commutative Noetherian ring $A$, $A\supset \Q$, $B=A/I$ and ${\bf G}(I)$ the associated graded ring to $I$. It is known that $H_{2}(A,B,B)=0$ is equivalent to $I$ being syzygetic. We prove that the vanishing of $\hd$ is equivalent to $I$ being of linear type and $\sigma _{3,q}:\extp{3}{B}{I/I^{2}}\otimes _{B}I^{q}/I^{q+1}\rightarrow \tor{3}{A}{B}{A/I^{q+1}}$, the $(3,q)$-antisymmetrization morphism, being surjective for all $q\geq 0$. Using this and a theorem of Ulrich on a conjecture of Herzog, we deduce that, in a regular local ring $A$, a Gorenstein, licci ideal $I$ verifies $\hd =0$ if and only if $I$ is a complete intersection. Thus, we characterize perfect (respectively, Gorenstein) ideals of grade two (respectively, three) with $\hd =0$ as those ideals which are of linear type (respectively, complete intersection). With any grade, but small deviation, we show that a licci ideal, generically a complete intersection and of deviation one, verifies $\hd =0$. This is not true for licci ideals of linear type and of deviation two. Commutative ringsAlgebra, HomologicalHomology of commutative ringsideal of linear typeAnells commutatiusHomologia, Teoria d'Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theoryClassificació AMS::13 Commutative rings and algebras::13D Homological methods Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/ Article

# Related documents

## Other documents of the same author

Planas Vilanova, Francesc d'Assís; O'Carroll, Liam
Giral, José M; Planas Vilanova, Francesc d'Assís
Muiños, Ferran; Planas Vilanova, Francesc d'Assís
O'Carroll, Liam; Planas Vilanova, Francesc d'Assís; Villarreal Rodríguez, Rafael Heraclio
Planas Vilanova, Francesc d'Assís

Coordination

Supporters