相关论文: A remark on singularities of primitive cohomology …

The Hard Lefschetz theorem for intersection cohomology of nonrational polytopes was recently proved by K. Karu [Ka]. This theorem implies the conjecture of R. Stanley on the unimodularity of the generalized $h$-vector. In this paper we…

We prove two general decomposition theorems for fixed-point invariants: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar additivity results for these invariants. Moreover, the proofs of…

The cohomology groups of Lie superalgebras and, more generally, of color Lie algebras, are introduced and investigated. The main emphasis is on the case where the module of coefficients is non-trivial. Two general propositions are proved,…

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for…

We give a natural notion of nondegeneracy for singular points of integrable non-Hamiltonian systems, and show that such nondegenerate singularities are locally geometrically linearizable and deformation rigid in the analytic case. We…

We construct natural operators connecting the cohomology of the moduli spaces of stable Higgs bundles with different ranks and genera which, after numerical specialization, recover the topological mirror symmetry conjecture of…

We introduce new boundary conditions for differential forms on symplectic manifolds with boundary. These boundary conditions, dependent on the symplectic structure, allows us to write down elliptic boundary value problems for both…

Local cohomology functors are constructed for the category of cohomological functors on an essentially small triangulated category T equipped with an action of a commutative noetherian ring. This is used to establish a local-global…

We define a cobordism theory in algebraic geometry based on normal crossing degenerations with double point singularities. The main result is the equivalence of double point cobordism to the theory of algebraic cobordism previously defined…

We develop a Helmholtz-like theorem for differential forms in Euclidean space $E_{n}$ using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannian manifolds, $R_{n}$, which, by virtue of the…

We prove a Lefschetz (1,1)-Theorem for proper seminormal varieties over the complex numbers. The proof is a non-trivial geometric argument applied to the isogeny class of the Lefschetz 1-motive associated to the mixed Hodge structure on…

We introduce the restricted local volume of a relatively very ample invertible sheaf as an invariant of equisingularity by determining its change across families. We apply this result to give numerical control of Whitney-Thom (differential)…

We study the Lefschetz standard conjecture on a smooth complex projective variety X. In degree 2, we reduce it to a local statement concerning deformations of vector bundles on X. When X is hyperk\"ahler, we show that the existence of…

We provide new local characterizations of Hida families of Siegel modular forms with genus two arising from automorphic inductions (stable Yoshida lifts), analogous to the characterizations of Hida families of CM modular forms provided by…

General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…

This paper investigates the relationship between the solvability of first-order differential equations and the topology of the underlying domain through the lens of de\,Rham cohomology. We analyze the conditions under which a closed 1-form…

A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category…

We prove -under certain conditions (local-global compatibility and vanishing of integral cohomology), a generalization of a theorem of Galatius and Venkatesh. We consider the case of GL(N) over a CM field and we relate the localization of…

In this paper we use the deformation to the normal cone and the corresponding Verdier-Saito specialization to define and study (spectral) Hirzebruch-Milnor type homology characteristic classes for local complete intersections. Our main…

We develop geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. Geometric approach clarifies several questions, e.g. the notion of homological unit…