Related papers: The effective Chen ranks conjecture

This works concerns cohomological support varieties of modules over commutative local rings. The main result is that the support of a derived tensor product of a pair of differential graded modules over a Koszul complex is the join of the…

We present a sharpened version of the Cohen-Gabber theorem for equicharacteristic, complete local domains (A,m,k) with algebraically closed residue field and dimension d > 0. Namely, we show that for any prime number p, Spec(A) admits a…

In this paper we study Koszul cohomology and the Green and Prym-Green conjectures for canonical and Prym-canonical binary curves. We prove that if property $N_p$ holds for a canonical or a Prym-canonical binary curve of genus $g$ then it…

We prove in a unifying way several equivalent descriptions of Koszul rings, some of which being well known in the literature. Most of them are stated in terms of coring theoretical properties of $\Tor_n^A(R,R)$. As an application of these…

Let R be a polynomial ring and M a finitely generated graded R-module of maximal grade (which means that the ideal I_t(\cA) generated by the maximal minors of a homogeneous presentation matrix, \cA, of M has maximal codimension in R).…

Let X and Y be finite-type CW-complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k-rescaling of the rational cohomology ring of X. Assume H^*(X,Q) is a Koszul algebra. Then, the homotopy Lie…

We study the exactness of certain combinatorially defined complexes which generalize the Orlik-Solomon algebra of a geometric lattice. The main results pertain to complex reflection arrangements and their restrictions. In particular, we…

We investigate a generalization of the classical notion of a Schur functor associated to a ribbon diagram. These functors are defined with respect to an arbitrary algebra, and in the case that the underlying algebra is the…

We prove an analogue of Koszul duality for category $\mathcal{O}$ of a reductive group $G$ in positive characteristic $\ell$ larger than 1 plus the number of roots of $G$. However there are no Koszul rings, and we do not prove an analogue…

For any ideal $I$ of finite projective dimension in a commutative noetherian local ring $R$, we prove that if the conormal module $I/I^2$ has finite projective dimension over $R/I$, then $I$ must be generated by a regular sequence. This…

We give a complete picture of the interaction between Koszul and Ringel dualities for quasi-hereditary algebras admitting linear tilting (co)resolutions of standard and costandard modules. We show that such algebras are Koszul, that the…

Given a quasi-hereditary algebra $B$, we present conditions which guarantee that the algebra $\gr B$ obtained by grading $B$ by its radical filtration is Koszul and at the same time inherits the quasi-hereditary property and other good…

In this paper, we prove that Ruan's Cohomological Crepant Resolution Conjecture holds for the Hilbert-Chow morphisms. There are two main ideas in the proof. The first one is to use the representation theoretic approach proposed in [QW]…

The Countable Telescope Conjecture arose in the framework of stable homotopy theory, as a tool conceived to study the chromatic filtration. It turned out, however, to trigger extremely fertile research within the framework of Module…

It it shown that the Bloch-Kato conjecture on the norm residue homomorphism $K^M(F)/l \to H^*(G_F,Z/l)$ follows from its (partially known) low-degree part under the assumption that the Milnor K-theory algebra $K^M(F)/l$ modulo $l$ is…

We show that the Koszul calculus of a preprojective algebra, whose graph is distinct from A$\_1$ and A$\_2$, vanishes in any (co)homological degree $p>2$. Moreover, its (higher) cohomological calculus is isomorphic as a bimodule to its…

Let $H$ be a finite dimensional pointed rank one Hopf algebra of nilpotent type. We first determine all finite dimensional indecomposable $H$-modules up to isomorphism, and then establish the Clebsch-Gordan formulas for the decompositions…

We briefly survey recent results related to linear series on curves that are general in various moduli spaces, highlighting the interplay between algebraic geometry on a general curve and the combinatorics of its degenerations.…

In this paper we prove that if G is a connected, simply-connected, semi-simple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra (Ug)_0 of the…

This paper proves that the nearby cycles complexes on a certain family of PEL local models are central with respect to the convolution product of sheaves on the corresponding affine flag varieties. As a corollary, the semisimple trace…