Related papers: Vinberg's $\theta$-groups and rigid connections

We construct the natural Frobenius structures on two families of rigid irregular $\check{G}$-connections on $\mathbb{G}_m$ (or $\mathbb{A}^1$) for a split simple group $\check{G}$: (i) the $\theta$-connections arising from Vinberg's…

We show that the Frenkel-Gross connection on $\mathbb{G}_m$ is physically rigid as $\check{G}$-connection, thus confirming the de Rham version of a conjecture of Heinloth-Ng\^o-Yun. The proof is based on the construction of the Hecke…

Let $G$ be a reductive group, and let $X$ be a smooth quasi-projective complex variety. We prove that any $G$-irreducible, $G$-cohomologically rigid local system on $X$ with finite order abelianization and quasi-unipotent local monodromies…

We review the Kohno-Drinfeld theorem as well as a conjectural analogue relating quantum Weyl groups to the monodromy of a flat connection D on the Cartan subalgebra of a complex, semi-simple Lie algebra g with poles on the root hyperplanes…

Let X_0 be a compact connected Riemann surface of genus g with D_0\subset X_0 an ordered subset of cardinality n, and let E_G be a holomorphic principal G-bundle on X_0, where G is a complex reductive affine algebraic group, that admits a…

Under some suitable assumptions Riemannian manifolds $(M, g, H)$ that admit a connection $\hat\nabla$ with torsion a 3-form $H$, which is both closed $d H=0$ and $\hat\nabla$-covariantly constant, are locally isometric to a product $N\times…

The relationship between comodules of a coring and flat connections is reviewed. In particular we specialise to corings which are built on a tensor product of algebra and a coalgebra. Such corings are in one-to-one correspondence with…

Let $K$ be a finite extension of ${\mathbb Q}_p$ and let $X$ be Drinfel'd's symmetric space of dimension $d$ over $K$. Let $\Gamma\subset {\rm SL}_{d+1}(K)$ be a cocompact discrete (torsionfree) subgroup and let…

Let $\mathbb{F}_{\Theta }=G/P_{\Theta }$ be a flag manifold associated to a non-compact real simple Lie group $G$ and the parabolic subgroup $% P_{\Theta }$. This is a closed subgroup of $G$ determined by a subset $% \Theta $ of simple…

An irreducible integrable connection $(E,\nabla)$ on a smooth projective complex variety $X$ is called rigid if it gives rise to an isolated point of the corresponding moduli space $\mathcal{M}_{dR}(X)$. According to Simpson's motivicity…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…

In this paper we construct a connection on the trivial G-bundle on the projective line for any simple complex algebraic group G, which is regular outside of the points 0 and infinity, has a regular singularity at the point 0, with principal…

Let $f: X \to S$ be flat morphism over an algebraically closed field $k$ with a relative normal crossings divisor $Y\subset X$, $(E, \nabla)$ be a bundle with a connection with log poles along $Y$ and curvature with values in…

We pursuit the research line proposed in \cite{YZ-Gflat} about the classification of Hermitian manifolds whose $s$-Gauduchon connection $\nabla^s =(1-\frac{s}{2})\nabla^c + \frac{s}{2}\nabla^b$ is flat, where $s \in \mathbb{R}$ and…

In this paper we investigate the arithmetic aspects of the theory of $\mathcal{E}_K^\dagger$-valued rigid cohomology introduced and studied in [11,12]. In particular we show that these cohomology groups have compatible connections and…

We define Frobenius and monodromy operators on the de Rham cohomology of $K$-dagger spaces (rigid spaces with overconvergent structure sheaves) with strictly semistable reduction $Y$, over a complete discrete valuation ring $K$ of mixed…

The group $\mathfrak{X}(G)$ is obtained from $G\ast G$ by forcing each element $g$ in the first free factor to commute with the copy of $g$ in the second free factor. We make significant additions to the list of properties that the functor…

A wide generalization of the classical theorem of A. Grothendieck asserting that for any faithfully flat extension of commutative rings, the corresponding relative Picard group and the Amitsur 1-cohomology group with values in the…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…

Flat connections for unitary gauge groups on a 3--torus with twisted boundary conditions as well as recently discovered periodic nontrivial flat connections with ``nondiagonalizable'' triples of holonomies for higher orthogonal and…