Zobrazeno 1 - 10
of 303
pro vyhledávání: '"Huneke, Craig"'
We provide a natural criterion which implies equality of the finitistic test ideal and test ideal in local rings of prime characteristic. Most notably, we show that the criterion is met by every local weakly $F$-regular ring whose anti-canonical alge
Externí odkaz:
http://arxiv.org/abs/2301.02202
Publikováno v:
Research in the Mathematical Sciences 8.4 (2021): 1-15
Let $(R,\mathfrak{m},\mathbb{k})$ be an equicharacteristic one-dimensional complete local domain over an algebraically closed field $\mathbb{k}$ of characteristic 0. R. Berger conjectured that R is regular if and only if the universally finite module
Externí odkaz:
http://arxiv.org/abs/2201.13002
Publikováno v:
In Advances in Mathematics April 2024 441
Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence, and thus satisfy the stable Harbourne Conjecture. In prime characteristic, we can take any radical ideal defining a Gorenst
Externí odkaz:
http://arxiv.org/abs/2007.12051
If I is an ideal in a Gorenstein ring S and S/I is Cohen-Macaulay, then the same is true for any linked ideal I'. However, such statements hold for residual intersections of higher codimension only under very restrictive hypotheses, not satisfied eve
Externí odkaz:
http://arxiv.org/abs/2001.05089
We explore the classical Lech's inequality relating the Hilbert--Samuel multiplicity and colength of an $\mathfrak{m}$-primary ideal in a Noetherian local ring $(R,\mathfrak{m})$. We prove optimal versions of Lech's inequality for sufficiently deep i
Externí odkaz:
http://arxiv.org/abs/1907.08344
We give explicit criteria that imply the resurgence of a self-radical ideal in a regular ring is strictly smaller than its codimension, which in turn implies that the stable version of Harbourne's conjecture holds for such ideals. This criterion is u
Externí odkaz:
http://arxiv.org/abs/1903.12122
We investigate the existence of ideals $I$ in a one-dimensional Gorenstein local ring $R$ satisfying $\mathrm{Ext}^{1}_{R}(I,I)=0$.
Comment: 17 pages
Comment: 17 pages
Externí odkaz:
http://arxiv.org/abs/1804.00939
Publikováno v:
Transactions of the American Mathematical Society, Series B. 10/23/2023, Vol. 10, p1333-1355. 23p.
We study conjectured generalizations of a formula of Lech which relates the multiplicity of a finite colength ideal in an equicharacteristic local ring to its colength, and prove one of these generalizations involving the multiplicity of the maximal
Externí odkaz:
http://arxiv.org/abs/1711.06951