Related papers: Cox-Gorenstein algebras
We prove a Poincar\'e duality for arithmetic $p$-adic pro-\'etale cohomology of smooth dagger curves over finite extensions of ${\mathbf Q}_p$. We deduce it, via the Hochschild-Serre spectral sequence, from geometric comparison theorems…
S. Alesker has shown that if $G$ is a compact subgroup of O(n) acting transitively on the unit sphere $S^{n-1}$ then the vector space $Val^G$ of continuous, translation-invariant, $G$-invariant convex valuations on $R^n$ has the structure…
The notions of $\mathbb Q$-Gorenstein scheme and of $\mathbb Q$-Gorenstein morphism are introduced for locally Noetherian schemes by dualizing complexes and (relative) canonical sheaves. These cover all the previously known notions of…
We show that generalised Calabi-Yau dg (co)algebras are Koszul dual to generalised symmetric dg (co)algebras, without needing to assume any smoothness or properness hypotheses. Similarly, we show that Gorenstein and Frobenius are Koszul…
Given a standard graded algebra over a field, we consider the relationship between G-quadraticity and the existence of a Koszul filtration. We show that having a quadratic Gr\"obner basis implies the existence of a Koszul filtration for…
We prove that Ext^*_A(k,k) is a Gerstenhaber algebra, where A is a Hopf algebra. In case A=D(H) is the Drinfeld double of a finite dimensional Hopf algebra H, our results implies the existence of a Gerstenhaber bracket on H^*_{GS}(H,H).…
We present a new approach to Poincare duality for Cuntz-Pimsner algebras. We provide sufficient conditions under which Poincare self-duality for the coefficient algebra of a Hilbert bimodule lifts to Poincare self-duality for the associated…
We introduce and investigate multicomplex configurations, a class of projective varieties constructed via specialization of the polarizations of Artinian monomial ideals. Building upon geometric polarization and geometric vertex…
We show that Rabinowitz Floer homology and cohomology carry the structure of a graded Frobenius algebra for both closed and open strings. We prove a Poincar\'e duality theorem between homology and cohomology that preserves this structure.…
The aim is to study Perazzo hypersurfaces $X=V(F)\subseteq\mathbb{P}(K^5)$, defined by $F(x_0,x_1,x_2,u,v) = p_0(u,v)x_0+p_1(u,v)x_1+p_2(u,v)x_2+g(u,v)$, where $p_0,p_1,p_2$ are algebraically dependent, but linearly independent forms of…
A class of classical affine W-algebras are shown to be isomorphic as differential algebras to the coordinate rings of double coset spaces of certain prounipotent proalgebraic groups. As an application, integrable Hamiltonian hierarchies…
Hochschild two-cocycles play an important role in the deformation \`a la Gerstenhaber of associative algebras. The aim of this paper is to introduce the category of Hoch-algebras whose objects are associative algebras equipped with an extra…
We prove that $p$-adic geometric pro-\'etale cohomology of smooth partially proper rigid analytic varieties over $p$-adic fields seen in the category of Topological Vector Spaces satisfies a Poincar\'e duality as we have conjectured. This…
The Grothendieck group of the tower of symmetric group algebras has a self-dual graded Hopf algebra structure. Inspired by this, we introduce by way of axioms, a general notion of a tower of algebras and study two Grothendieck groups on…
Macaulay's Inverse System gives an effective method to construct Artinian Gorenstein k-algebras. To date a general structure for Gorenstein k-algebras of any dimension (and codimension) is not understood. In this paper we extend Macaulay's…
Let F be a locally compact nonarchimedean field with residue characteristic p and G the group of F-rational points of a connected split reductive group over F. For k an arbitrary field, we study the homological properties of the…
We prove duality theorems for twisted Reidemeister torsions and twisted Alexander polynomials generalizing the results of Turaev. As a corollary we determine the parity of the degrees of twisted Alexander polynomials of 3-manifolds in many…
We describe graded commutative Gorenstein algebras ${\mathcal E}_n(p)$ over a field of characteristic $p$, and we conjecture that $\mathrm{Ext}^\bullet_{\mathsf{Ver}_{p^{n+1}}}(1,1)\cong{\mathcal E}_{n}(p)$, where $\mathsf{Ver}_{p^{n+1}}$…
In this paper, we investigate Lefschetz properties of Veronese subalgebras. We show that, for a sufficiently large $r$, the $r$\textsuperscript{th} Veronese subalgebra of a Cohen-Macaulay standard graded $K$-algebra has properties similar…
We consider two families of polynomials that play the same role in the Temperley Lieb algebra of a Coxeter group as the Kazhdan Lusztig and R polynomials play in the Hecke algebra of the group. We study these polynomials from a…