The Buchsbaum-Eisenbud-Horrocks Conjecture predicts that if M is a non-zero module of finite length and finite projective dimension over a local ring R of dimension d, then the i-th Betti number of M is at least d choose i. This conjecture implies th...

Document(s)

Title

Hochster's theta invariant is defined for a pair of finitely generated modules on a hypersurface ring having only an isolated singularity. Up to a sign, it agrees with the Euler invariant of a pair of matrix factorizations. Working over the complex n...

The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing ℚ, we describe K *(R[t])/K *(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology. We use t...

What's the probability that two elements in a finite group commute? A formal answer, Pr2(G) = {(x, y) [element of] G2 |xy = yx}| / |G|2 begs our next question. How many ordered pairs of elements of a finite group commute?

We give conditions for the Mayer–Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties and schemes, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to topological cyclic ...

If the finite group G acts on the finite non-empty set X (i.e., G is represented as a group of permutations of X), then ....

In this paper we compute the probability that an n-tuple for a group G is S-rewritable for a given set S of permutations for several classes of groups.

Let $Q$ be a commutative, Noetherian ring and $Z \subseteq \operatorname{Spec}(Q)$ a closed subset. Define $K_0^Z(Q)$ to be the Grothendieck group of those bounded complexes of finitely generated projective $Q$-modules that have homology supported on...

Udgivelsesdato: 2007-Aug

Udgivelsesdato: 2007-Aug