For a Noetherian local domain (R, m, K), it is an open question whether strong F–regularity deforms. We provide an affirmative answer to this question when the canonical module satisfies certain additional assumptions. The techniques used here involve passing to a Gorenstein ring, using an anti– canonical cover.

In this article we investigate when a complete ideal in a twodimensional regular local ring is a multiplier ideal of some ideal with an integral multiplying parameter. In particular, we show that this question is closely connected to the Gorenstein property of the blowup along the ideal.

A toric face ring, which generalizes both Stanley-Reisner rings and affine semigroup rings, is studied by Bruns, Römer and their coauthors recently. In this paper, under the “normality” assumption, we describe a dualizing complex of a toric face ring R in a very concise way. Since R is not a graded ring in general, the proof is not straightforward. We also develop the squarefree module theory o...

The so-called ’change-of-ring’ results are well-known expressions which present several connections between projective, injective and flat dimensions over the various base rings. In this note we extend these results to the Gorenstein dimensions over Cohen-Macaulay local rings.

The subalgebra of the tautological ring of the moduli of curves of compact type generated by the κ classes is studied. Relations, constructed via the virtual geometry of the moduli of stable maps, are used to prove universality results relating the κ rings in genus 0 to higher genus. Predictions for κ classes of the Gorenstein conjecture are proven.

In this paper, we discuss on the existence of filtrations of modules having good properties. In particular, we focus on filtered homomorphisms called strict, and show that there exists a filtration which makes a filtered homomorphism a strict filtered homomorphism. Moreover, by using this result, we study purity for filtered modules over a Gorenstein filtered ring.

We prove, assuming Greenberg’s conjecture, that the ordinary eigencurve is Gorenstein at an intersection point between the Eisenstein family and the cuspidal locus. As a corollary, we obtain new results on Sharifi’s conjecture. This result is achieved by constructing a universal ordinary pseudodeformation ring and proving an R = T result.