… In this paper, we consider the singularity category Dsg (mod A) and the Z-graded … explicitly
its ordinary singularity category Dsg(modA) by using the triangulated orbit categories of type A …

… Now we describe how to compute a standard basis for a set of germs in either of the
following local rings: fractional germs R[x, λ]〈x,λ〉, formal power series R[[x, λ]], and …

… if its local ring is a regular local ring. A fundamental problem is to remove a singularity by
simple … giving a proof of resolution of surface singularities in positive characteristic in Chapter 7. …

… Matrix factorizations were introduced by Eisenbud [14] and used by Buchweitz [4] for the
purposes of the study of maximal Cohen–Macaulay modules over hypersurface local rings. …

… equivalence between their singularity categories, we … singularity equivalent, see Theorem
3.5. Besides, with the help of [17], we also use (Q, Sp, I) to describe the singularity categories …

… be a left and right noetherian ring. Later on Rickard proved in … , this category is triangle-equivalent
to the stable category of A… singularity of the algebra A, we call it the singularity category …

… If A can be chosen to be commutative, we just take as A the local ring C~X, Y]/f(X, Y) of a
simple plane curve singularity. The computations of many of these Auslander-Reiten quivers …

… the relative stable category of and the usual singularity category for group algebras with …
noetherian ring. When the coefficient ring is self-injective we show that these categories share a …

… In particular, if the germ 67xx is a local ring for every xe X, we call (X, 6x) a locally ringed
space. A pair (p, q,”) : (X, 6x) → (Y, 67)) is called a morphism of ringed spaces if p : X → Y is a …

… that R is weakly F-regular if and only if the local rings Rm are … F-regularity are equivalent for
a local ring, it is sufficient to … , since it is also known that a local ring is weakly F-regular if and …