… We investigate the behavior of singularity categories and stable categories of Gorenstein …
a morphism of rings. The natural context to approach the problem is via change of rings, that is, …

… A has enough projectives (as for example in the cases of modules over dg rings we will
be studying later) any cotorsion pair cogenerated by a set is automatically small: …

… Accordingly, our central motivation is to generalize the definition of singularity category by
replacing R with a DGA or a ring spectrum. The fundamental difficulty is that of giving good …

… the ring R∆, which is not changed if we change the variables x, y and z by a linear base
change with coefficients in C. Our first aim of here is therefore to work in a graded setting in order …

… the singularity category: one can define the singularity cate… ], who coined the name “singularity
category”. Orlov shows that … noetherian ring, its dg singularity category is the dg category …

… Numerical invariants of a singularity. Suppose R is a noetherian local ring. Then it is well-…
adThe multiplicity is a positive integer and is equal to 1 if and only if R is a regular local ring. …

… 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 …

… Striking similarities had suggested a connection between rings with rational singularities
and rings in which all (or certain) ideals are tightly closed. Both are preserved upon passing to …

… ring op is contained in one and only one valuation ring R of the function field Q(C), where Q
is the universal domain. The complete local ring o… local ring for a two-branch singularity at P. …

… different options in Singularity for computational rings, ie, polynomial, fractional, formal power
series and smooth germ rings, that they each can be used by commands in Singularity for …