Related papers: A stacky $p$-adic Riemann--Hilbert correspondence …

We study the spectral location of strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide"…

We prove a Hitchin-Kobayashi correspondence for affine vortices generalizing a result of Jaffe-Taubes for the action of the circle on the affine line. Namely, suppose a compact Lie group K has a Hamiltonian action on a Kaehler manifold X…

Let $k$ be an algebraic closure of finite fields with odd characteristic $p$ and a smooth projective scheme $\mathbf{X}/W(k)$. Let $\mathbf{X}^0$ be its generic fiber and $X$ the closed fiber. For $\mathbf{X}^0$ a curve Faltings conjectured…

Let X/k be an abelian variety over an algebraically closed field k of characteristic p > 0. In this paper, using the Azumaya property of the sheaf of crystalline differential operators and the Morita equivalence, we show that etale locally…

We study resolutions of the rational map to the moduli space of stable curves that associates with a point in the Hitchin base the spectral curve. In the rank two case the answer is given in terms of the space of quadratic multi-scale…

For a complex reductive group $G$, we consider the locus $M^d$ in the moduli stack of $G$-Higgs bundles on which the centraliser dimension of the Higgs field takes a constant value $d> rk(G)$. We describe a non-abelian structure for the…

Let $K$ be a finite extension of the $p$-adic numbers $\mathbb Q_p$ with ring of integers $\mathcal O_K$, $\mathcal X$ a regular scheme, proper, flat, and geometrically irreducible over $\mathcal O_K$ of dimension $d$, and $\mathcal X_K$…

It was shown by Diaconescu, Donagi and Pantev that Hitchin systems of type ADE are isomorphic to certain Calabi-Yau integrable systems. In this paper, we prove an analogous result in the setting of meromorphic Hitchin systems of type A…

The Kontsevich-Soibelman solution of the cyclic version of Deligne's conjecture and the formality of the operad of little discs on a cylinder provide us with a natural homotopy calculus structure on the pair (C^*(A), C_*(A)) ``Hochschild…

We prove an orbifold type decomposition theorem for the Hochschild homology of the symmetric powers of a small DG category $\mathcal{A}$. In noncommutative geometry, these can be viewed as the noncommutative symmetric quotient stacks of…

Let $\varphi\colon X\rightarrow Y$ be a degree two Galois cover of smooth curves over a local field $F$ of odd characteristic. Assuming that $Y$ has good reduction, we describe a semi-stability criterion for the curve $X$, using the data of…

We prove an analogue of the Kobayashi-Hitchin correspondence oncompact connected 3-folds that is fibered on orbifold Riemann surfaces and satisfy an integrability condition, which contains compact connected Sasakian 3-folds. We define…

For a variety $X$ separated over a perfect field of characteristic $p>0$ which admits an embedding into a smooth variety, we establish an anti-equivalence between the bounded derived categories of Cartier crystals on $X$ and constructible…

Let $X$ be a compact connected Riemann surface and $D$ an effective divisor on $X$. Let ${\mathcal N}_H(r,d)$ denote the moduli space of $D$-twisted stable Higgs bundles (a special class of Hitchin pairs) on $X$ of rank $r$ and degree $d$.…

Let $X$ be a smooth projective complex curve, $P\subset X$ a reduced effective divisor, and $X^{0}=X\setminus P$. We study logarithmic $V$-twisted Higgs bundles arising from a logarithmic Hecke compactification of a rank-two bundle on…

Let $k$ be an algebraic closure of a finite field of odd characteristic. We prove that for any rank two graded Higgs bundle with maximal Higgs field over a generic hyperbolic curve $X_1$ defined over $k$, there exists a lifting $X$ of the…

We consider the theory of Lax equations in complex simple and reductive classical Lie algebras with the spectral parameter on a Riemann surface of finite genus. Our approach is based on the new objects -- the Lax operator algebras, and…

This paper is the second in a series of four papers aiming to describe the (almost integral) Chow ring of $\Mbar_3$, the moduli stack of stable curves of genus $3$. In this paper, we introduce the moduli stack $\Htilde_g^r$ of hyperelliptic…

Let G be a connected semisimple linear algebraic group over an algebraically closed field k of positive characteristic and let X denote an equivariant embedding of G. We define a distinguished Steinberg fiber N in G, called the zero-fiber,…

Let $X$ be a compact connected Riemann surface of genus at least two and $G$ a connected reductive complex affine algebraic group. The Riemann--Hilbert correspondence produces a biholomorphism between the moduli space ${\mathcal M}_X(G)$…