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Melvin Hochster

  1. Ideals Generated by Quadratic Polynomials.

    Tue, 06/07/2011 - 15:01 — SomNambul
    Authors: Melvin Hochster, Tigran Ananyan
    Subjects: Commutative Algebra
    Abstract

    Let $R$ be a polynomial ring in $N$ variables over an arbitrary field $K$ and
    let $I$ be an ideal of $R$ generated by $n$ polynomials of degree at most 2. We
    show that there is a bound on the projective dimension of $R/I$ that depends
    only on $n$, and not on $N$.

  2. Homological invariants of modules over contracting endomorphisms.

    Mon, 10/18/2010 - 15:01 — SomNambul
    Authors: Srikanth B. Iyengar, Luchezar L. Avramov, Yongwei Yao, Melvin Hochster
    Subjects: Commutative Algebra
    Abstract

    It is proved that when R is a local ring of positive characteristic, $\phi$
    is its Frobenius endomorphism, and some non-zero finite R-module has finite
    flat dimension or finite injective dimension for the R-module structure induced
    through $\phi$, then R is regular.

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