A survey of test ideals
By Karl Schwede, Kevin Tucker. 2011
79 citations recorded by the source corpus.
Test ideals were first introduced by Mel Hochster and Craig Huneke in their celebrated theory of tight closure, and since their invention have been closely tied to the theory of Frobenius splittings. Subsequently, test ideals have also found application far beyond their original scope to questions arising in complex analytic geometry. In this paper we give a contemporary survey of test ideals and their wide-ranging applications.
Subfields: Computer Science Applications, Media Technology
View Paper: https://www.semanticscholar.org/paper/811b7daa324ede7028de0a831a248f7916221a3f
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Citations in the corpus
- A canonical linear system associated to adjoint divisors in characteristic $p > 0$ (2011, unknown): “−→ OX, where Le,∆ = OX((1 − pe)(KX + ∆)) is a line bundle. Conversely, given a map φ: Fe ∗ L −→ OX, it uniquely determines an effective Q-divisor ∆φ such that OX ((1 −pe)(KX +∆)) ∼= L. See [Sch09a] or [ST11] for further discussion. In this context however, τ(X,∆) is the unique smallest non-zero ideal”
- F-signature of pairs and the asymptotic behavior of Frobenius splittings (2011, background): “ analog of the multiplier ideal from higher dimensional algebraic geometry. Likewise, the subscheme defined by the splitting prime is analogous to the minimal LC-center. For additional discussion, see [ST11]. 3. F-signature The F-signature of a local ring Ris a numerical invariant which, roughly spea”
- Semi-positivity in positive characteristics (2012, background): “ties. As mentioned in the introduction, these are characteristic pcounterparts of the singularities of the minimal model program. We give only the minimally needed definitions, we re fer the reader to [ST11] for a general survey on the theory of F-singularities. As the singularities of the minimal mo”
- F-signature and Hilbert–Kunz multiplicity : a combined approach and comparison (2016, unknown): “The crucial step and main technical result is Theorem 6.3, which uses the uniformity of the constants tracked above to swap limits between iterations of Frobenius and progression in an approximately Gorenstein sequence.”
- On the three dimensional minimal model program in positive characteristic (2013, background): “exciting progress in both commutative algebra and birational geometry (see for example the survey paper [ST11] and the references therein).”