Related papers: $\ell$-adic local systems and Higgs bundles: the g…

We use Scholze's framework of diamonds to gain new insights in correspondences between $p$-adic vector bundles and local systems. Such correspondences arise in the context of $p$-adic Simpson theory in the case of vanishing Higgs fields. In…

Let $X$ be a smooth irreducible projective curve of genus $g \geq 2$ over a finite field $\F_{q}$ of characteristic $p$ with $q$ elements such that the function field $\F_{q}(X)$ is a geometric Galois extension of the rational function…

Let \(X\) be an irreducible smooth complex projective variety, and let \(G\) be a connected reductive linear algebraic group over \(\mathbb{C}\). In this paper, we first classify integrable transitive algebraic Lie algebroids on $X$. We…

Let $H$ be a connected semisimple linear algebraic group defined over $\mathbb C$ and $X$ a compact connected Riemann surface of genus at least three. Let ${\mathcal M}'_X(H)$ be the moduli space parametrising all topologically trivial…

A theorem of Weil and Atiyah says that a holomorphic vector bundle $E$ on a compact Riemann surface $X$ admits a holomorphic connection if and only if the degree of every direct summand of $E$ is zero. Fix a finite subset $S$ of $X$, and…

We describe moduli spaces of logarithmic rank $2$ connections on elliptic curves with $n \geq 1$ poles and generic residues. In particular, we generalize a previous work by the first and second named authors. Our main approach is to analyze…

We consider the moduli space of stable parabolic Higgs bundles of rank $r$ and fixed determinant, and having full flag quasi-parabolic structures over an arbitrary parabolic divisor on a smooth complex projective curve $X$ of genus $g$,…

We study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if…

We consider all irreducible rank-4 hypergeometric local systems defined over $\mathbb{Q}$ that support a rational one-dimensional variation of Hodge structures of weight 3 and Hodge vector $(1,1,1,1)$. Up to a natural equivalence there are…

Given a generic stable strongly parabolic $SL(2,\mathbb{C})$-Higgs bundle $(\mathcal{E}, \varphi)$, we describe the family of harmonic metrics $h_t$ for the ray of Higgs bundles $(\mathcal{E}, t \varphi)$ for $t\gg0$ by perturbing from an…

Let $\ell$ be an odd prime and $K$ a field of characteristic different from $\ell$. Let $\bar{K}$ be an algebraic closure of $K$. Assume that $K$ contains a primitive $\ell$th root of unity. Let $n \ne \ell$ be another odd prime. Let $f(x)$…

Let $X$ be a compact Riemann surface of genus $g \geq 3$ and $S$ a finite subset of $X$. Let $\xi$ be fixed a holomorphic line bundle over $X$ of degree $d$. Let $\mathcal{M}_{pc}(r, d, \alpha)$ (respectively, $\mathcal{M}_{pc}(r, \alpha,…

In this paper we describe the structure of the space of parabolic reductions, and their compactifications, of principal $G$-bundles over a smooth projective curve over an algebraically closed field of arbitrary characteristic. We first…

We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…

Let H be a complex Lie group acting holomorphically on a complex analytic space X such that the restriction to X_{\mathrm{red}} of every H-invariant regular function on X is constant. We prove that an H-equivariant holomorphic vector bundle…

We study topologically trivial $G$-Higgs bundles over an elliptic curve $X$ when the structure group $G$ is a connected real form of a complex semisimple Lie group $G^{\mathbb{C}}$. We achieve a description of their (reduced) moduli space,…

Let $\mathcal{L}=(L,[\cdot\,,\cdot],\delta)$ be an algebraic Lie algebroid over a smooth projective curve $X$ of genus $g\geq 2$ such that $L$ is a line bundle whose degree is less than $2-2g$. Let $r$ and $d$ be coprime numbers. We prove…

Let $X$ be a normal geometrically connected variety over a finite field $\kappa$ of characteristic~$p$. Let $E$ be a number field. Using automorphic methods over global function fields, we derive properties of the geometric monodromy groups…

We show that a two dimensional $\ell $-adic representation of the absolute Galois group of a number field which is locally potentially equivalent to a $GL(2)$-$\ell$-adic representation $\rho$ at a set of places of $K$ of positive upper…

We consider the local model of a Shimura variety of PEL type, with the unitary similitudes corresponding to a ramified quadratic extension of $\mathbb{Q}_p$ as defining group. We examine the cases where the level structure at $p$ is given…