SOME RESEARCH MANUSCRIPTS

Below are links for PostScript files of some research manuscripts. (The order is roughly reverse chronological.) The author's research papers on this site were all prepared while the author was partially supported by grants from the National Science Foundation. The current grant is DMS-0901145.


A preprint of the manuscript Ideals generated by quadratic polynomials (with Tigran Ananayan).


A preprint of the manuscript Homological invariants of modules over contracting endomorphisms (with L. Aramov, S. Iyengar, and Y. Yao) to appear in Mathematische Annalen.


A preprint of the manuscript An embedding theorem for modules of finite projective dimension (with Y. Yao).


A preprint of the manuscript The F-rational signature and drops in the Hilbert-Kunz multiplicity (with Y. Yao).


A preprint of the manuscript Second coefficients of Hilbert-Kunz functions for domains (with Y. Yao).


A preprint of the manuscript Test exponents for modules with finite phantom projective dimension (with Y. Yao).


A preprint of the manuscript Local cohomology with support in a parameter ideal (with Y. Yao).


A preprint of the manuscript Tight closure in equal characteristic zero   (with C. Huneke, 204 pages).


A preprint of the manuscript Quasilength, latent regular sequences, and content of local cohomology (with C. Huneke), Journal of Algebra 322 (2009) 3170-3193.


A preprint of the manuscript The Frobenius structure of local cohomology, (with F. Enescu), Algebra & Number Theory 2 (2008) 721-754.


A preprint of the manuscript Fine behavior of symbolic powers of ideals (with C. Huneke) Illinois J. Math. 51 (2007), 171--183.


A preprint of the manuscript Some finiteness properties of Lyubeznik's F-modules, Proceedings of the Midwest Algebraic Geometry Seminar, 2005 (MAGIC05) Contemp. Math 448. Amer. Math. Soic., Providence, R.I., 2007, 119-127.


A preprint of the manuscript Lower bounds for Betti numbers of special extensions   (with B. Richert), Journal of Pure and Applied Algebra 201 (2005) 328-339.


A preprint of the manuscript Diamond closure   (with J. Velez), in Algebra, Arithmetic and Geometry with Applications, Papers from Shreeram S. Abhyankar's 70th Birthday Conference, Springer-Verlag, Berlin - Heidelberg - New York, 2004, pp. 511-523.


A preprint of the manuscript Parameter-like sequences and extensions of tight closure   in Commutative Ring Theory and Applications (Proc. of the Fourth International Conference, held in Fez, Morocco, June 7-12, 2001), Marcel Dekker, New York, 2003, pp. 267-287.


A preprint of the manuscript Big Cohen-Macaulay algebras in dimension three via Heitmann's theorem,   Journal of Algebra 254 (2002) 395-408.


A preprint of the manuscript Presentation depth and the Lipman-Sathaye Jacobian Theorem,   Homology, Homotopy and Applications (International Press, Cambridge, MA) Vol. 4 (2002) 295-314.


A preprint of the manuscript Comparison of symbolic and ordinary powers of ideals   (with C. Huneke), Inventiones Math. 147 (2002) 349-369.


A preprint of the manuscript Localization and test exponents for tight closure  (with C. Huneke), Michigan Math. J. 48 (2000) 305-329.


A preprint of the manuscript The tight integral closure of a set of ideals,   J. of Algebra 230 (2000) 184-203.


A preprint of the manuscript Failure of coherence and finite Tor dimension in absolute integral closures   (with Ian M. Aberbach), Journal of Pure and Applied Algebra (memorial issue for H. Matsumura) 122 (1997), 171-184.


Solid Closure,   in Commutative Algebra: Syzygies, Multiplicities and Birational Algebra, Contemp. Math. 159, Amer. Math. Soc., Providence, R. I., 1994, 103-172.


F-regularity, test elements, and smooth base change   (with C. Huneke), Trans. Amer. Math. Soc. 346 (1994), 1-62.


Indecomposable canonical modules and connectedness   (with C. Huneke), in Commutative Algebra: Syzygies, Multiplicities and Birational Algebra, Contemp. Math. 159, Amer. Math. Soc., Providence, R. I., 1994, 197-208.


Absolute integral closures are big Cohen-Macaulay algebras in characteristic p   (with
C. Huneke), Bull. Amer. Math. Soc. (New Series) 24 (1991), 137-143.