We investigate the behavior of the test ideal of an excellent reduced ring of prime characteristic under base change. It is shown that if h : A ?! D is a smooth homomorphism, then A D = D , assuming that all residue elds of A at maximal ideals are perfect and that formation of the test ideal commutes with localization. It is also shown that if h : (A; m) ?! D is a nite at homomorphism of Gorens...

We provide a (mostly) self-contained treatment of Hochster and Huneke’s theorem characterizing Hilbert-Kunz multiplicity in terms of tight closure. This is not a new proof, just an elaboration of the one given in [3].

Introduction: This study is designed to explore the biomechanical principles of posterior bilateral pedicle screw on steps progressively and tight closure on every step for severe angular kyphosis and the indication conditions and clinical pathways of above new technique. Materials and Methods: A total of 90 patients have severe angular kyphosis, 37 males and 53 females, with an average age of ...

We prove a version of Fujita’s Conjecture in arbitrary characteristic, generalizing results of K.E. Smith. Our methods use the Frobenius morphism, but avoid tight closure theory. We also obtain versions of Fujita’s Conjecture for coherent sheaves with certain ampleness properties.

We give a treatment of the Brenner-Monsky example based on polynomial algebra and linear algebra. No prior knowledge of tight closure theory, Hilbert-Kunz theory, algebraic geometry or local cohomology is assumed.

Hara [Ha3] and Smith [Sm2] independently proved that in a normal Q-Gorenstein ring of characteristic p ≫ 0, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair (R,∆) of a normal ring R and an effective Q-Weil divisor ∆ on SpecR. As a corollary, we obtain the equivalence of strongly F-regular pairs and klt pairs.

It is an open question whether tight closure commutes with localization in quotients of a polynomial ring in finitely many variables over a field. Katzman [K] showed that tight closure of ideals in these rings commutes with localization at one element if for all ideals I and J in a polynomial ring there is a linear upper bound in q on the degree in the least variable of reduced Gröbner bases in...

Adherens and tight junctions play key roles in assembling epithelia and maintaining barriers. In cell culture zonula occludens (ZO)-family proteins are important for assembly/maturation of both tight and adherens junctions (AJs). Genetic studies suggest that ZO proteins are important during normal development, but interpretation of mouse and fly studies is limited by genetic redundancy and/or a...