Related papers: On the Locus of Hodge Classes

Let $X$ be a smooth irreducible quasi-projective algebraic variety over a number field $K$. Suppose $X$ is equipped with a $p$-adic \'{e}tale local system compatible with an admissible graded-polarized variation of mixed Hodge structures on…

A Hopf Galois structure on a finite field extension $L/K$ is a pair $(H,\mu)$, where $H$ is a finite cocommutative $K$-Hopf algebra and $\mu$ a Hopf action. In this paper we present a program written in the computational algebra system…

Let A be an abelian fourfold. We prove the Standard Conjecture of Hodge type for A. By combining this result with a theorem of Clozel we deduce that numerical equivalence on A coincides with l-adic homological equivalence on A for…

Let $A$ be an Abelian variety of dimension $n$. For $0<p<2n$ an odd integer, Sampson constructed a surjective homomorphism $\pi :J^p(A)\rightarrow A$, where $J^p(A)$ is the higher Weil Jacobian variety of $A$. Let $\widehat{\omega}$ be a…

We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…

We know that semi-regular sub-varieties satisfy the variational Hodge conjecture i.e., given a family of smooth projective varieties $\pi:\mathcal{X} \to B$, a special fiber $\mathcal{X}_o$ and a semi-regular subvariety $Z \subset…

The codomain category of a generalized homology theory is the category of modules over a ring. For an abelian category A, an A-valued (generalized) homology theory is defined by formally replacing the category of modules with the category…

The topological Hochschild homology THH(R) of a commutative S-algebra (E_infty ring spectrum) R naturally has the structure of a commutative R-algebra in the strict sense, and of a Hopf algebra over R in the homotopy category. We show,…

Let H be a coFrobenius Hopf algebra over a field k. Let A be a right H-comodule algebra over k. We recall that the category of right H-comodules admits a certain model structure whose homotopy category is equivalent to the stable category…

There is no systematic general procedure by which isomorphism classes of Hopf algebras that are extensions of $\k F$ by ${\k}^G$ can be found. We develop the general procedure for classification of isomorphism classes of Hopf algebras which…

The present article takes advantage of the properties of algebras in the category of S-modules (twisted algebras) to investigate further the fine algebraic structure of Hopf operads. We prove that any Hopf operad P carries naturally the…

We prove that a finite-dimensional irreducible Hopf algebra $H$ in positive characteristic is semisimple, if and only if it is commutative and semisimple, if and only if the restricted Lie algebra $P(H)$ of the primitives is a torus. This…

A comodule algebra P over a Hopf algebra H with bijective antipode is called principal if the coaction of H is Galois and P is H-equivariantly projective (faithfully flat) over the coaction-invariant subalgebra B. We prove that principality…

Let $A$ be a differential graded algebra with cohomology ring $H^*A$. A graded module over $H^*A$ is called \emph{realisable} if it is (up to direct summands) of the form $H^*M$ for some differential graded $A$-module $M$. Benson, Krause…

Let $A$ be a simple C*-algebra of stable rank one and let $p$ and $q$ be two $\sigma$-compact open projections. It is proved that there is a continuous path of unitaries in ${\tilde A}$ which connects open sub-projections of $p$ which is…

It is shown that Nichols algebras over alternating groups A_m, m>4, are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to A_m is isomorphic to the group…

An algebraic theory $T$ is a category with objects $t_0,t_2...$ such that for each $n$ the object $t_n$ is an $n$-fold categorical product of $t_1$. A strict $T$-algebra is a product preserving functor $A: T\to Spaces$. Lawvere showed that…

We provide a closed form expression for linear Hodge integrals on the hyperelliptic locus. Specifically, we find a succinct combinatorial formula for all intersection numbers on the hyperelliptic locus with one $\lambda$-class, and powers…

We prove that the structure algebra of a Bruhat moment graph of a finite real root system is a Hopf algebroid with respect to the Hecke and the Weyl actions. We introduce new techniques (reconstruction and push-forward formula of a product,…

We show that a conjecture by Lawson holds, that is, the inclusion from the Chow variety $C_{p,d}(P^n)$ of all effective algebraic p-cycles of degree d in n-dimensional projective space to the space of effective algebraic p-cycles is…