Related papers: Comparison of Dualizing Complexes

For a group $G$ (of type $F$) acting properly on a coarse Poincar\'{e} duality space $X$, Kapovich-Kleiner introduced a coarse version of Alexander duality between $G$ and its complement in $X$. More precisely, the cohomology of $G$ with…

Let D be a divisor in a complex analytic manifold X. A natural problem is to determine when the de Rham complex of meromorphic forms on X with poles along D is quasi-isomorphic to its subcomplex of logarithmic forms. In this mostly…

We consider the analogue of Kutasov-Schwimmer-Seiberg duality for two-dimensional $\mathcal{N}=(2,2)$ $U(k)$ gauge theory with one adjoint $X$ with the superpotential $\Tr X^{l+1}$ and with fundamental and anti-fundamantal chiral…

Let M be a real analytic manifold, F a bounded complex of constructible sheaves. We show that the Whitney-de Rham complex associated to F is quasi-isomorphic to F.

Building on our previous work, we investigate an analogue of the differential symbol map used in the Bloch-Gabber-Kato theorem. Within this framework, for an appropriate variety over a field, the higher Chow group corresponds to the 0-th…

Let $K$ be one of the complex classical groups ${\rm O}_k$, ${\rm GL}_k$, or ${\rm Sp}_{2k}$. Let $M \subseteq K$ be the block diagonal embedding ${\rm O}_{k_1} \times \cdots \times {\rm O}_{k_r}$ or ${\rm GL}_{k_1} \times \cdots \times…

We study deformations of holomorphic maps of compact, complex, K\"ahler manifolds. In particular, we describe a generalization of Bloch's semiregularity map that annihilates obstructions to deform holomorphic maps with fixed codomain.

We prove a polynomial bound in the "true complexity" problem of Gowers and Wolf. The proof uses only repeated applications of the Cauchy--Schwarz inequality, answering negatively a question posed by Gowers and Wolf. To choose and reason…

We present a nearby cycle sheaf construction in the context of symmetric spaces. This construction can be regarded as a replacement for the Grothendieck-Springer resolution in classical Springer theory.

We study the interplay of the homotopy coniveau tower, the Rost-Schmid complex of a strictly homotopy invariant sheaf, and homotopy modules. For a strictly homotopy invariant sheaf $M$, smooth $k$-scheme $X$ and $q \geqslant 0$ we construct…

We study the structure of the relative Hilbert scheme for a family of nodal (or smooth) curves via its natural cycle map to the relative symmetric product. We show that the cycle map is the blowing up of the discriminant locus, which…

Using Totaro-Bloch-Kriz's linear fractional cycles Gangl and Muller-Stach recently prove the 5-term relations for the dilogarithm in Bloch's higher Chow group CH^2(F,3) and the Kummer-Spence relations in some group G(F) over an arbitrary…

We display a symmetric monoidal equivalence between the stable $\infty$-category of filtered spectra, and quasi-coherent sheaves on $\mathbb{A}^1 / \mathbb{G}_m$, the quotient in the setting of spectral algebraic geometry, of the flat…

We define the grove polynomials, a set-valued extension of forest polynomials. We show that they are $K$-theoretically dual to the quasisymmetric Schubert cells which pave the quasisymmetric flag variety, in the same way that Grothendieck…

In this paper, we generalize the Dirac-dual-Dirac method to Hecke pairs with equivariant coarse embeddings and establish the K-theoretic isomorphisms between the maximal and reduced equivariant Roe algebras. We also extend these results to…

We develop semiclassical methods to analyze the spectrum of BPS monopole operators for superconformal field theories in three dimensions with N=2 supersymmetry. We show that the chiral ring of the theory results from the semiclassical…

We investigate boundedness results for families of holomorphic symplectic varieties up to birational equivalence. We prove the analogue of Zarhin's trick by for $K3$ surfaces by constructing big line bundles of low degree on certain moduli…

Based on Balmer's tensor triangular Chow group, we propose K-theoretic Chow groups of derived categories of noetherian schemes and their Milnor variants for regular schemes and their thickenings. We discuss functoriality and show that our…

We prove an extension of the Kato-Saito class field theory for smooth projective schemes over a finite field to schemes with singularities. As an application, we obtain Bloch's formula for the Chow groups of 0-cycles on such schemes. We…

We prove relations between fractional linear cycles in Bloch's integral cubical higher Chow complex in codimension two of number fields, which correspond to functional equations of the dilogarithm. These relations suffice, as we shall…