Yongwei Yao's Research

Research interests

Commutative algebra: Tight closure, Frobenius closure, and Hilbert-Kunz multiplicity theories over Noetherian rings of prime characteristic p; and general primary decomposition theories over Noetherian rings.

Publications and preprints

• Uniform test exponents in rings of finite F-representation type, preprint.
  — .pdf file.
• A weak embedding theorem (and test exponents) for modules of finite phantom projective dimension (with Melvin Hochster), work in progress
  — work in progress.
• Generic local duality and purity exponents (with Melvin Hochster), preprint.
• An embedding theorem for modules of finite projective dimension (with Melvin Hochster), preprint.
  — .pdf file.
• Second coefficients of Hilbert-Kunz functions for domains (with Melvin Hochster), preprint.
  — .pdf file.
• On a generalizatin of Ulrich modules and its applications (with Ela Celikbas, Olgur Celikbas, Justin Lyle and Ryo Takahashi), preprint.
  — pdf file.
• On the vanishing of (co)homology for modules admitting certain filtrations (with Olgur Celikbas), J. Pure Appl. Algebra 229 (2025)
  — .pdf file.
• Graded rings of rational twist in prime characteristic (with Florian Enescu), J. Pure Appl. Algebra 228 (2024)
  — .pdf file.
• Injective capacity and cogeneration (with Robin Baidya), accepted by Proc. Amer. Math. Soc..
  — .pdf file.
• Frobenius splitting, strong F-regularity, and small Cohen-Macaulay modules (with Melvin Hochster), Trans. Amer. Math. Soc. 376 (2023) no. 9, 6729–6765.
  — .pdf file.
• Global Frobenious Betti numbers and Frobenius Euler characteristics (with Alessandro De Stefani and Thomas Polstra), Mich. Math. J. 71 (2022) no. 3, 533–552.
  — .pdf file.
• F-rational signature and drops in the Hilbert-Kunz multiplicity (with Melvin Hochster), Algebra and Number Theory 16 (2022) no. 8, 1777–1809.
  — .pdf file.
• Global F-spltting ratio of modules (with Alessandro De Stefani and Thomas Polstra), J. Algebra 610 (2022), 773–792.
  — .pdf file.
• Globalizing F-invariants (with Alessandro De Stefani and Thomas Polstra), Adv. in Math. 350 (2019), 359–395.
  — available on arXiv (arXiv:1608.08580).
• Lech's inequality, the Stückrad-Vogel conjecture, and uniform behavior of Koszul homology (with Patricia Klein, Linquan Ma, Pham Hung Quy and Ilya Smirnov), Adv. in Math. 347 (2019), 442–472.
  — available on arXiv (arXiv:1808.01051).
• Tensoring with the Frobenius endomorphism (with Olgur Celikbas and Arash Sadeghi), Homology, Homotopy and Applications 20 (2018) no. 1, 251–257.
  — available on arXiv (arXiv:1706.00238).
• Generalizing Serre's Splitting Theorem and Bass's Cancellation Theorem via free-basic elements (with Alessandro De Stefani and Thomas Polstra), Proc. Amer. Math. Soc. 146 (2018) no. 4, 1417–1430.
  — available on arXiv (arXiv:1608.08591).
• On the Frobenius complexity of determinantal rings (with Florian Enescu), J. Pure Appl. Algebra, 222 (2018) no. 2, 414–432.
  — .pdf file. Also available on arXiv (arXiv:1503.03164).
• Some extensions of Hilbert-Kunz multiplicity (with Neil Epstein), Collect. Math. 68 (2017) no. 1, 69–85.
  — .pdf file.
• The Frobenius complexity of a local ring of prime characteristic (with Florian Enescu), J. Algebra, 459 (2016), 133–156.
  — .pdf file. Also available on arXiv (arXiv:1401.0234).
• Local cohomology with support in a parameter ideal (with Melvin Hochster), J. Pure Appl. Algebra 217 (2013) no. 4, 664–671.
  — .pdf file.
• Test exponents for modules with finite phantom projective dimension (with Melvin Hochster), Illinois J. Math. 56 (2012) no. 4, 1095–1107.
  — .pdf file.
• Criteria for flatness and injectivity (with Neil Epstein), Math. Z. 271 (2012) no. 3, 1193–1210.
  — .pdf file.
• The compatibility, independence, and linear growth properties, book volume `Progress in Commutative Algebra: Ring Theory, Homology, and Decompositions' by de Gruyter.
  — .pdf file.
• Homological invariants of modules over contracting endomorphisms (with Luchezar L. Avramov, Melvin Hochster and Srikanth B. Iyengar), Math. Ann. 353 (2012) no. 2, 275–291.
  — .pdf file.
• The lower semicontinuity of the Frobenius splitting numbers (with Florian Enescu), Math. Proc. Cambridge Philos. Soc. 150 (2011) no. 1, 35–46.
  — .pdf file.
• Infinite rings with planar zero-divisor graphs, Comm. Algebra 36 (2008) no. 11, 4068–4077.
  — .pdf file.
• The direct sum decomposability of  ^eM in dimension 2, Michigan Math. J., Special volume in honor of Melvin Hochster, 57 (2008), 745–755.
  — .pdf file.
• Frobenius test exponents for parameter ideals in generalized Cohen-Macaulay local rings (with C. Huneke, M. Katzman, and R. Y. Sharp), J. Algebra 305 (2006), 516–539.
  — .pdf file.
• Observations on the F-signature of local rings of characteristic p, J. Algebra 299 (2006), 198–218.
  — .pdf file.
• Primary decomposition II: primary components and linear growth, J. Pure Appl. Algebra 205 (2006) no. 1, 226–242.
  — .pdf file.
• Modules with finite F-representation type, J. London Math. Soc. (2) 72 (2005), no. 1, 53–72.
  — .pdf file.
• Primary decomposition: compatibility, independence and linear growth, Proc. Amer. Math. Soc. 130 (2002) no. 6, 1629–1637.
  — .pdf file.
• Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular (with Craig Huneke), Proc. Amer. Math. Soc. 130 (2002) no. 3, 661–665.
  — .pdf file.