Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Counterexamples to the Eisenbud–Goto regularity conjecture
HTML articles powered by AMS MathViewer

by Jason McCullough and Irena Peeva HTML | PDF
J. Amer. Math. Soc. 31 (2018), 473-496 Request permission


Our main theorem shows that the regularity of nondegenerate homogeneous prime ideals is not bounded by any polynomial function of the degree; this holds over any field $k$. In particular, we provide counterexamples to the longstanding Regularity Conjecture, also known as the Eisenbud–Goto Conjecture (1984). We introduce a method which, starting from a homogeneous ideal $I$, produces a prime ideal whose projective dimension, regularity, degree, dimension, depth, and codimension are expressed in terms of numerical invariants of $I$. The method is also related to producing bounds in the spirit of Stillman’s Conjecture, recently solved by Ananyan and Hochster.
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 13D02
  • Retrieve articles in all journals with MSC (2010): 13D02
Additional Information
  • Jason McCullough
  • Affiliation: Mathematics Department, Iowa State University, Ames, Iowa 50011
  • MR Author ID: 790865
  • Irena Peeva
  • Affiliation: Mathematics Department, Cornell University, Ithaca, New York 14853
  • MR Author ID: 263618
  • Received by editor(s): September 21, 2016
  • Received by editor(s) in revised form: August 24, 2017
  • Published electronically: November 10, 2017
  • Additional Notes: The second author was partially supported by NSF grants DMS-1406062 and DMS-1702125.
  • © Copyright 2017 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 31 (2018), 473-496
  • MSC (2010): Primary 13D02
  • DOI:
  • MathSciNet review: 3758150