Related papers: The integral Hodge polygon for $p$-divisible group…

In arXiv:1709.07504 Ardila and Aguiar give a Hopf monoid structure on hypergraphs as well as a general construction of polynomial invariants on Hopf monoids. Using these results, we define in this paper a new polynomial invariant on…

Let $p$ be an odd prime. For field extensions $L/\mathbb{Q}_p$ with Galois group isomorphic to the dihedral group $D_{2p}$ of order $2p$, we consider the problem of computing a basis of the associated order in each Hopf Galois structure and…

Given an irreducible well-generated complex reflection group, we construct an explicit basis for the module of vector fields with logarithmic poles along its reflection arrangement. This construction yields in particular a Hodge filtration…

The Hilbert class polynomial $H_{\mathcal{O}}(x)\in \mathbb{Z}[x]$ attached to an order $\mathcal{O}$ in an imaginary quadratic field $K$ is the monic polynomial whose roots are precisely the distinct $j$-invariants of elliptic curves over…

Fix a smooth projective family of curves $C \to S$ and a split reductive group scheme $G$ over a Noetherian base scheme $S$. For any (possibly nonreduced) fixed relative Cartier divisor $D$, we provide a treatment of the moduli of…

The purpose of this work is to geometrize the notion of mixed Hodge structure. Therefore, we associate equivariant vector bundles on the projective plane to trifiltered vector spaces. Making this Rees construction with filtrations arising…

Igusa noted that the Hasse invariant of the Legendre family of elliptic curves over a finite field of odd characteristic is a solution mod $p$ of a Gaussian hypergeometric equation. We show that any family of exponential sums over a finite…

Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and uniform treatment of certain known results on Hodge…

Let $G$ be a finite group, $p$ a prime, and $k$ a field of characteristic $p$. We introduce the notion of an endotrivial chain complex of $p$-permutation $kG$-modules, which are the invertible objects in the bounded homotopy category of…

Let $G$ be a finite $p$-group, where $p$ is an odd prime number, $H$ be a subgroup of $G$ and $\theta\in \Irr(H)$ be an irreducible character of $H$. Assume also that $|G:H|=p^2$. Then the character $\theta^G$ of $ G$ induced by $\theta$ is…

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…

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. A holomorphic triple $(E_1,E_2,\phi)$ on $X$ consists of two holomorphic vector bundles $E_{1}$ and $E_{2}$ over $X$ and a holomorphic map $\phi \colon E_{2}…

The Hodge series of a finite matrix group is the generating function for invariant exterior forms of specified order and degree. Lauret, Miatello, and Rossetti gave examples of pairs of non-conjugate cyclic groups having the same Hodge…

Based on some analogies with the Hodge theory of isolated hypersurface singularities, we define Hodge-type numerical invariants (called H-numbers) of any, not necessarily algebraic, link in $S^3$. They contain the same information as the…

In this note we consider the flat bundle U and the kernel K of the Higgs field naturally associated to any (polarized) variation of Hodge structures of weight 1. We study how strict the inclusion of U in K can be in the geometric case. More…

We study a pair of Calabi-Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence D^b(X) = D^b(M), building on work of Gross, Popescu, Bak, and Schnell. Over the complex numbers, X…

We consider in this paper a relative version of the Howe-Moore Property, about vanishing at infinity of coefficients of unitary representations. We characterize this property in terms of ergodic measure-preserving actions. We also…

We describe the possible Mordell-Weil groups for degree 1 elliptic threefold with rational base and constant $j$-invariant. Moreover, we classify all such elliptic threefolds if the $j$-invariant is nonzero. We can use this classification…

A variation of Hodge structure is a horizontal holomorphic mapping into a flag domain D; here "horizontal" indicates that the image of the map satisfies a system of partial differential equations known as the infinitesimal period relation…

In this article, the Hodge decomposition for any degree of differential forms is investigated on the whole space $\mathbb{R}^n$ and the half-space $\mathbb{R}^n_+$ on different scale of function spaces namely homogeneous and inhomogeneous…