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pro vyhledávání: '"Aberbach, Ian M."'
In this paper we prove that the Watanabe-Yoshida conjecture holds up to dimension $7$. Our primary new tool is a function, $\varphi_J\left(R; z^t\right),$ that interpolates between the Hilbert-Kunz multiplicities of a base ring, $R$, and various radi
Externí odkaz:
http://arxiv.org/abs/2402.05822
Autor:
Aberbach, Ian M., Sarkar, Parangama
Let $(R,\mathfrak m)$ be a local (Noetherian) ring of dimension $d$ and $M$ a finite length $R$-module with free resolution $G_\bullet$. De Stefani, Huneke, and N\'{u}\~{n}ez-Betancourt explored two questions about the properties of resolutions of $M
Externí odkaz:
http://arxiv.org/abs/1810.02526
Let $(R,m)$ be a local Noetherian ring, let $M$ be a finitely generated $R$-module and let $(F_{\bullet},\partial_{\bullet})$ be a free resolution of $M$. We find a uniform bound $h$ such that the Artin-Rees containment $I^n F_i\cap Im \, \partial_{i
Externí odkaz:
http://arxiv.org/abs/1406.2866
Autor:
Aberbach, Ian M., Enescu, Florian
Publikováno v:
Nagoya Math. J. 212 (2013), 59-85
We present results on the Watanabe-Yoshida conjecture for the Hilbert-Kunz multiplicity of a local ring of positive characteristic. By improving on a "volume estimate" giving a lower bound for Hilbert-Kunz multiplicity, we obtain the conjecture when
Externí odkaz:
http://arxiv.org/abs/1101.5078
Autor:
Aberbach, Ian M., Hosry, Aline
Publikováno v:
Journal of Algebra, 345 (2011), 72-80
The Brian\c{c}on-Skoda theorem in its many versions has been studied by algebraists for several decades. In this paper, under some assumptions on an F-rational local ring $(R,\m)$, and an ideal $I$ of $R$ of analytic spread $\ell$ and height $g < \el
Externí odkaz:
http://arxiv.org/abs/1010.1062
Autor:
Aberbach, Ian M., Hosry, Aline
Publikováno v:
Proc. Amer. Math. Soc., 139 (2011), 3903-3907
We generalize a Brian\c{c}on-Skoda type theorem first studied by Aberbach and Huneke. With some conditions on a regular local ring $(R,\m)$ containing a field, and an ideal $I$ of $R$ with analytic spread $\ell$ and a minimal reduction $J$, we prove
Externí odkaz:
http://arxiv.org/abs/1010.1061
Autor:
Aberbach, Ian M., Enescu, Florian
Let $(R,\m)$ be a formally unmixed local ring of positive prime characteristic and dimension $d$. We examine the implications of having small Hilbert-Kunz multiplicity (i.e., close to 1). In particular, we show that if $R$ is not regular, there exist
Externí odkaz:
http://arxiv.org/abs/0708.0537
Autor:
Aberbach, Ian M., Enescu, Florian
We show that the F-signature of an F-finite local ring R of characteristic p >0 exists when R is either the localization of an $\mathbf{N}$-graded ring at its irrelevant ideal or $\mathbf{Q}$-Gorenstein on its punctured spectrum. This extends results
Externí odkaz:
http://arxiv.org/abs/math/0502351
We study the relation type question, raised by C. Huneke, which asks whether for a complete equidimensional local ring R there exists a uniform bound for the relation type of parameter ideals. Wang gave a positive answer to this question when the non
Externí odkaz:
http://arxiv.org/abs/math/0501477
Autor:
Aberbach, Ian M., Enescu, Florian
For a reduced F-finite ring R of characteristic p >0 and q=p^e one can write R^{1/q} = R^{a_q} \oplus M_q, where M_q has no free direct summands over R. We investigate the structure of F-finite, F-pure rings R by studying how the numbers a_q grow wit
Externí odkaz:
http://arxiv.org/abs/math/0310227