相关论文: Geometric methods for cohomological invariants
The Z_2-graded Cech cohomology theory is considered in the framework of noncommutative geometry over complex number field and in particular the homotopy invariance and Morita invariance are proven.
Let G be a finite group of exponent m and let k be a field of characteristic prime to m, containing the m-th roots of unity. For any Rost cycle module M over k, we construct exact sequences detecting the unramified elements in Serre's group…
Suppose $X$ is a hyperelliptic curve of genus $g$ defined over an algebraically closed field $k$ of characteristic $p=2$. We prove that the de Rham cohomology of $X$ decomposes into pieces indexed by the branch points of the hyperelliptic…
We use group homology to define invariants in algebraic K-theory and in an analogue of the Bloch group for Q-rank one lattices and for some other geometric structures. We also show that the Bloch invariants of CR structures and of flag…
We investigate the algebras of invariants and the properties of the quotient morphism by an action of a finite group scheme in terms of stabilizers of points.
We study cohomologies of a curve with an action of a finite $p$-group over a field of characteristic $p$. Assuming the existence of a certain 'magical element' in the function field of the curve, we compute the equivariant structure of the…
We introduce a general theory of homological Milnor-Witt cycle modules over an excellent base scheme equipped with a dimension function, extending both Rost's cycle modules and Feld's theory over fields. To any such module we associate a…
In the present paper, we examine in detail the method of "graph compactifications" of topological groups. The graph and Ellis methods of constructing proper compactifications of topological groups are applied for the investigation of…
We revisit the geometry of involutions in groups of finite Morley rank. Our approach unifies and generalises numerous results, both old and recent, that have exploited this geometry; though in fact, we prove much more. We also conjecture…
A strategy to address the inverse Galois problem over Q consists of exploiting the knowledge of Galois representations attached to certain automorphic forms. More precisely, if such forms are carefully chosen, they provide compatible…
Building on the algebraic framework developed by Hendricks, Manolescu, and Zemke, we introduce and study a set of Floer-theoretic invariants aimed at detecting corks. Our invariants obstruct the extension of a given involution over any…
For any smooth complex projective variety X and smooth very ample hypersurface Y in X, we develop the technique of genus zero relative Gromov-Witten invariants of Y in X in algebro-geometric terms. We prove an equality of cycles in the Chow…
We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients.…
A theory of Galois co-objects for von Neumann bialgebras is introduced. This concept is closely related to the notion of comonoidal W*-Morita equivalence between von Neumann bialgebras, which is a Morita equivalence taking the…
We propose an deepened analysis of KV-Poisson structures of on IR^2. We present their classification their properties an their possible applications in different domains. We prove that these structure give rise to a new Cohomological…
In this paper, we first discuss some properties of the Galois linear maps. We provide some equivalent conditions for Hopf algebras and Hopf (co)quasigroups as its applications. Then let $H$ be a Hopf quasigroup with bijective antipode and…
In the present notes we generalize the classical work of Demazure [Invariants sym\'etriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws. Let G be a split semisemiple linear…
In this paper, we present a novel method for co-clustering, an unsupervised learning approach that aims at discovering homogeneous groups of data instances and features by grouping them simultaneously. The proposed method uses the entropy…
We announce new methods for using prismatic cohomology to compute the K-groups of $\mathbb{Z}/p^n$ and related rings. We use computer algebra methods to compute these K-groups through a large range in specific cases and also obtain explicit…
We describe the deformation cohomology of a symplectic groupoid, and use it to study deformations via Moser path methods, proving a symplectic groupoid version of the Moser Theorem. Our construction uses the deformation cohomologies of Lie…