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- Tohoku UniversityJP12 papers
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5 papers · 1 filter
Multigraded rings, diagonal subalgebras, and rational singularities
Kazuhiko Kurano, Ei-ichi Sato, Anurag K. Singh +1
We study the properties of F-rationality and F-regularity in multigraded rings and their diagonal subalgebras. The main focus is on diagonal subalgebras of bigraded rings: these co…
Flat modules and Gröbner bases over truncated discrete valuation rings
Toshiro Hiranouchi, Yuichiro Taguchi
We present basic properties of Gröbner bases of submodules of a free module of finite rank over a polynomial ring with coefficients in a graded truncated discrete valuations ri…
F-thresholds, tight closure, integral closure, and multiplicity bounds
Craig Huneke, Mircea Mustata, Shunsuke Takagi +1
The F-threshold $c^J(\a)$ of an ideal $\a$ with respect to the ideal is a positive characteristic invariant obtained by comparing the powers of $\a$ with the Frobenius powers o…
D-modules over rings with finite F-representation type
Shunsuke Takagi, Ryo Takahashi
Smith and Van den Bergh introduced the notion of finite F-representation type as a characteristic analogue of the notion of finite representation type. In this paper, we prove…
On F-pure thresholds
Shunsuke Takagi, Kei-ichi Watanabe
Using the Frobenius map, we introduce a new invariant for a pair $(R,\a)$ of a ring and an ideal $\a \subset R$, which we call the F-pure threshold $\mathrm{c}(\a)$ of $\a$, an…