Related papers: On the Bott-Chern characteristic classes for coher…

We develop a framework to compute characteristic classes and their forms in the computer algebra system SageMath using symbolic calculus. In order to do this, we make use of the Chern-Weil approach in which characteristic classes of vector…

Transitive Lie algebroids have specific properties that allow to look at the transitive Lie algebroid as an element of the object of a homotopy functor. Roughly speaking each transitive Lie algebroids can be described as a vector bundle…

We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological…

We investigate the set of (real Dolbeault classes of) balanced metrics $\Theta$ on a balanced manifold $X$ with respect to which a torsion-free coherent sheaf $\mathcal{E}$ on $X$ is slope stable. We prove that the set of all such $[\Theta]…

We show that the Taylor-Wiles method can be applied to the cohomology of a Shimura variety $S$ of PEL type attached to a unitary similitude group $G$, with coefficients in the coherent sheaf attached to an automorphic vector bundle $\CF$ ,…

We show that the hypercohomology of most character twists of perverse sheaves on a complex abelian variety vanishes in all non-zero degrees. As a consequence we obtain a vanishing theorem for constructible sheaves and a relative vanishing…

Let S be a smooth projective surfaces and S^[n] the Hilbert scheme of zero-dimensional subschemes of S of length n. We proof that the class of S^[n] in the complex cobordism ring depends only on the class of the surface itself. Moreover, we…

We show that certain characteristic varieties of a finitely generated module over a given Weyl algebra arising from weighted degree filtrations are equal to the critical cone of some other characteristic varieties. This behaviour of the…

Let $R$ be a ring and Ch($R$) the category of chain complexes of $R$-modules. We put an abelian model structure on Ch($R$) whose homotopy category is equivalent to $K(Proj)$, the homotopy category of all complexes of projectives. However,…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

For a connected regular scheme X, flat and of finite type over Spec(Z), we construct a reciprocity homomorphism \rho_X: C_X --> \pi_1^\ab(X), which is surjective and whose kernel is the connected component of the identity. The (topological)…

It is proved that the category of simplicial complete bornological spaces over $\mathbb R$ carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is…

We use the theory of cubic structures to give a fixed point Riemann-Roch formula for the equivariant Euler characteristics of coherent sheaves on projective flat schemes over Z with a tame action of a finite abelian group. This formula…

We apply the algebraic consideration of holonomy systems to study Hermitian manifolds whose Chern connection is Ambrose-Singer and prove structure theorems for such manifolds. The main result (Theorem 1.2) asserts that the universal cover…

Supersymmetric heterotic string models, built from a Calabi-Yau threefold $X$ endowed with a stable vector bundle $V$, usually lead to an anomaly mismatch between $c_2(V)$ and $c_2(X)$; this leads to the question whether the difference can…

In this paper, we shall discuss possible theories of defining equivariant singular Bott-Chern classes and corresponding uniqueness property. By adding a natural axiomatic characterization to the usual ones of equivariant Bott-Chern…

We study derived categories of coherent sheaves on abelian varieties. We give a criterion for the equivalence of the derived categories on two abelian varieties. We describe the autoequivalence group for the derived category of coherent…

We construct Chern-Simons bundles as $\mathrm{Aut}^{+}P$-equivariant $U(1)$ -bundles with connection over the space of connections $\mathcal{A}_{P}$ on a principal $G$-bundle $P\rightarrow M$. We show that the Chern-Simons bundles are…

We construct Euler and Stiefel-Whitney classes of vector bundles with quadratic form by analyzing the intersection theory of the associated quadric bundles. We also compute the Chow rings of quadric and isotropic flag bundles. Along the…

For a finite group $G$, we compute the algebraic $K$-theory of the category of equivariant sheaves on a locally compact Hausdorff $G$-space, generalizing a result of Efimov, and determine the equivariant $E$-theory of the $C^*$-algebra of…