Related papers: Additive cycle complex and coherent duality

We construct a quasi-inverse of the cochain map on the negative cyclic complexes of the second kind induced from the quasi-Yoneda embedding on a curved dg algebra. This gives an explicit formula for the Chern character of a perfect module.

In this paper, we present necessary and sufficient combinatorial conditions for a link to be projective, that is, a link in $RP^3$. This characterization is closely related to the notions of antipodally self-dual and antipodally symmetric…

Let $K$ be an abelian extension of the rationals. Let $S(K)$ be the Schur group of $K$ and let $CC(K)$ be the subgroup of $S(K)$ generated by classes containing cyclic cyclotomic algebras. We characterize when $CC(K)$ has finite index in…

Let $V$ be a complete discrete valuation ring with residue field $\mathbb{F}$. We define a cyclic homology theory for algebras over $\mathbb{F}$, by lifting them to free algebras over $V$, which we enlarge to tube algebras and complete…

We introduce $k$-robust clique complexes, a family of simplicial complexes that generalizes the traditional clique complex. Here, a subset of vertices forms a simplex provided it does not contain an independent set of size $k$. We…

Let $f \colon X \to Y$ be a morphism of concentrated schemes. We characterize $f$-perfect complexes $\mathcal{E}$ as those such that the functor $\mathcal{E} \otimes^{\mathbf{L}}_X \mathbf{L} f^*-$ preserves bounded complexes. We prove, as…

Our aim is to give a fairly complete account on the construction of compatible model structures on exact categories and symmetric monoidal exact categories, in some cases generalizing previously known results. We describe the close…

This note proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. We apply this to categories of perfect complexes. It is shown that the bounded derived category of finitely presented…

We study the moduli space of coherent systems in $P^2$ using the Segre invariant. We obtain necessary conditions for the existence of $\alpha$-semistable coherent systems $(E,V)$ of type $(2, c_1, c_2, k)$, with $k \geq 2$. Afterwards, we…

We derive finite rational formulas for the traces of cycle integrals of certain meromorphic modular forms. Moreover, we prove the modularity of a completion of the generating function of such traces. The theoretical framework for these…

We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thick subcategories of the bounded derived category of a locally…

Due to the work of many authors in the last decades, given an algebraic orbifold (smooth proper Deligne-Mumford stack with trivial generic stabilizer), one can construct its orbifold Chow ring and orbifold Grothendieck ring, and relate them…

We define a filtration on the Chow groups of a smooth projective variety X over a field k by using the cycle map into continuous l-adic etale cohomology. The main theorem says that if k is a function field in one variable over a finite…

In this paper we show that Bloch's higher cycle class map with finite coefficients for quasi-projective equi-dimensional schemes over a field fits naturally in a long exact sequence involving Schreieder's refined unramified cohomology. We…

We prove that the $p$-adically completed periodic topological cyclic homology of a DG category over a perfect field $k$ of characteristic $p>2$ is isomorphic to the ($p$-adically completed) periodic cyclic homology of a lifting of the DG…

Let $X$ be a smooth proper scheme over an algebraically closed field $k$ in characteristic $p$. In this short note, by interpreting $\mathcal{D}_{X}$-modules as $F$-divided sheaves and establishing a cohomological boundedness property for…

In this largely expository paper we extend properties of the homological duality functor $RHom_{\mathcal H}(-,{\mathcal H})$ where ${\mathcal H}$ is the Hecke algebra of a reductive $p$-adic group, to the case where it is the Hecke algebra…

For a finite quiver without sources or sinks, we prove that the homotopy category of acyclic complexes of injective modules over the corresponding finite dimensional algebra with radical square zero is triangle equivalent to the derived…

A smooth intersection $Y$ of two quadrics in $\mathbb{P}^{2g+1}$ has Hodge level 1. We show that such varieties $Y$ have a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological…

Over a field of characteristic zero, we introduce two motivic operations on additive higher Chow cycles: analogues of the Connes boundary $B$ operator and the shuffle product on Hochschild complexes. The former allows us to apply the…