Geometric interpretation of tight closure and test ideals

By N. Hara. 2001

72 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/18d9808322ad856a91b727da4bb33aca45fbdd1b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Formulas for multiplier ideals on singular varieties (2004, unknown): “Theorem 1.13 ([HY, Theorem 6.8], cf.[ Ha1 ], [Sm]).”
F-adjunction (2009, background): “Big test ideals are characteristic p> 0 analogs of multiplier ideals, [Smith 2000; Hara 2001; Takagi 2004b; Hara and Yoshida 2003].”
Discreteness and rationality of F-jumping numbers on singular varieties (2009, background): “operties (see for example [HY03] and [Tak06]), but also diﬀers in some key ways (see [MY09]). Test ideals are rooted in the theory of tight closure of Hochster and Huneke [HH90], see also [Smi95] and [Har01]. The variants we are considering here were introduced in [HY03] and [Tak04]. Just as for mul”
On Hodge spectrum and multiplier ideals (2002, background): “ algebraic geometry (see [De95], [Si98], [Ei97], [Ka99], [EL99], [ELS01], [CEL01]). Recently, the multiplier ideals turned out to be connected with the test ideals of commutative algebra (see [Sm00], [H01], [Ta02]). For a survey, see [La01], where the algebraic theory of multiplier ideals is develop”
Test ideals in non-Q-Gorenstein rings (2009, background): “Furthermore, if one reduces X and a to characteristic p 0, then the multiplier ideal J ( X p ; a tp ) agrees with the big test ideal τ b ( R p ; a tp ) = (cid:2) τ ( R p , a tp ) (the big test ideal is also called the non-ﬁnitistic test ideal); see [Smi00], [Har01], [HY03], and [Tak04b].”
Integral closure of ideals, rings, and modules (2006, background): “It has been further studied in Hara [105], [106]; Smith [275]; Takagi [287]; Hara and Takagi [107]; and Hara and Watanabe [109].”
Centers of F-purity (2008, background): “Since test ideals are closely related to multiplier ideals (see [ 9 ,13,38,40]) it is natural to ask whether multiplier ideals (or even multiplier ideal-like constructions such as adjoint ideals, see [30,42]) always yield uniformly (�, F)-compatible ideals.”