The cohomological dimension of a resultant variety in prime characteristic \(p\)
type: Item
instance of: scholarly article
title: The cohomological dimension of a resultant variety in prime characteristic \(p\)
zbMATH Open document ID: 0902.13012
author: Mordechai Katzman
published in: Journal of Algebra
publication date: 1998-12-10T00:00:00Z
review text: Let \(k\) be a field and \(F_1(s,t),\dots, F_n(s,t)\) homogeneous polynomials of \(s\) and \(t\) with indeterminate coefficients \(X_1,\dots, X_l\). We consider the ideal \(I\) of \(A= k[X_1,\dots, X_k]\) obtained by eliminating \(s\) and \(t\) from \((F_1,\dots, F_n)\). If \(I\) is generated by \(m\) elements, then \(H_I^i(A)=0\) for \(i> m\). Thus the cohomological dimension of \(V(I)\) is a lower bound of the number of generators of \(I\). In this article, the author computes the cohomological dimension of \(V(I)\) by using the theory of \(F\)-modules when \(\text{char } k>2\), \(n=3\) and \(\deg F_1=\cdots= \deg F_3= 2\). The case of \(\text{char } k=0\) is studied by \textit{Z. Yan} in another article.
reviewed by: Takesi Kawasaki
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 13A35
Mathematics Subject Classification ID: 13E15
zbMATH DE Number: 1021748
zbMATH Keywords: cohomological dimension
zbMATH Keywords: number of generators
zbMATH Keywords: \(F\)-modules
MaRDI profile type: Publication
full work available at URL: jabr.1996.6951
OpenAlex ID: W2067740788
cites work: Bass Numbers of Local Cohomology Modules
cites work: The invariant theory of binary forms
cites work: Minimal resultant systems
DOI: 10.1006/JABR.1996.6951
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description: scientific article; zbMATH DE number 1021748