In arthropods, it is known that ecdysteroids regulate molting, limb regeneration, and reproduction through activation of the ecdysone receptor (EcR). However, the ecdysteroid signaling pathway for promotion of ovarian development in crustaceans is still unclear. In this study, three cDNA isoforms of EcR were cloned from the mud crab Scylla paramamosain. qRT-PCR revealed that the SpEcR mRNA was ...

Examples are given to show that the support of a complex of modules over a commutative noetherian ring may not be read off the minimal semi-injective resolution of the complex. These also give examples of semiinjective complexes whose localization need not be homotopically injective. Let R be a commutative noetherian ring. Recall that the support of a finitely generated R-module M is the set of...

Let R be an integral domain of finite type over Z and let f : X → SpecR be a smooth projective morphism of relative dimension d ≥ 1. We investigate, for a vector bundle E on the total space X , under what arithmetical properties of a sequence (pn, en)n∈N, consisting of closed points pn in SpecR and Frobenius descent data Epn ∼= F n(F) on the closed fibers Xpn , the bundle E0 on the generic fibe...

0→ Ps → · · · → Pi → 0 where each Pi is a finitely generated projective R-module. Let P the full subcategory of D consisting of complexes isomorphic to perfect complexes. These are precisely the compact objects, also called small objects, in D. These notes are an abstract of two lectures I gave at the workshop. The main goal of the lectures was to present various proofs of a theorem of Hopkins ...

LetR be a finitely generated commutative algebra over an algebraically closed field k and let A = R[t;σ, δ] be the Ore extension with respect to an automorphism σ and a σ-derivation δ. We view A as the coordinate ring of an affine non-commutative space X. The inclusion R → A gives an affine map ξ : X → SpecR, and X is a non-commutative analogue of A 1 ×SpecR. We define the fiber Xp of ξ over a ...

We initiate a unified, axiomatic study of noncommutative algebras R whose prime spectra are, in a natural way, finite unions of commutative noetherian spectra. Our results illustrate how these commutative spectra can be functorially “sewn together” to form SpecR. In particular, we construct a bimodule-determined functor ModZ → ModR, for a suitable commutative noetherian ring Z, from which there...

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.

This study investigated the combined effects of feeding ration and cheliped autotomy on intermolt duration, molting success, molt increments in size weight, ecdysteroid receptor gene (SpEcR) expression early juvenile mud crab Scylla paramamosain. Newly molted second stage crabs (C2) were subjected to four conditions; optimal, suboptimal (1/2 optimal), low (1/4 optimal) starvation, (intact vs. a...

Suppose that X = SpecR is an F -finite normal variety in characteristic p > 0. In this paper we show that the big test ideal τb(R) = τ̃ (R) is equal to ∑ ∆ τ(R; ∆) where the sum is over ∆ such that KX + ∆ is Q-Cartier. This affirmatively answers a question asked by various people, including Blickle, Lazarsfeld, K. Lee and K. Smith. Furthermore, we have a version of this result in the case that R...