Related papers: Special cycles for Shtukas are closed

We introduce and study (strict) Schottky G-bundles over a compact Riemann surface X, where G is a connected reductive algebraic group. Strict Schottky representations are shown to be related to branes in the moduli space of G-Higgs bundles…

We review the recent proof of the N.Takahashi's conjecture on genus $0$ Gromov-Witten invariants of $(\mathbb{P}^2, E)$, where $E$ is a smooth cubic curve in the complex projective plane $\mathbb{P}^2$. The main idea is the use of the…

Fix a smooth projective curve over a field of characteristic zero and a finite set of punctures. Let G be a connected linear algebraic group. We prove that the moduli of G-bundles with logarithmic connections having fixed residue classes at…

By Koebe's retrosection theorem, every closed Riemann surface of genus $g \geq 2$ is uniformized by a Schottky group. Marden observed that there are Schottky groups that are not classical ones, that is, they cannot be defined by a suitable…

Let $X$ be a smooth projective curve over an algebraically closed field $k$. Let $\mathcal{G}$ be a Bruhat-Tits group scheme on $X$ which is generically semi-simple and trivial. We show that the \'etale fundamental group of the moduli stack…

We construct an algebraic-cycle based model for the motivic cohomology on the category of schemes of finite type over a field, where schemes may admit arbitrary singularities and may be non-reduced. We show that our theory is functorial on…

Let X be a smooth variety over a field k, and l be a prime number invertible in k. We study the (\'etale) unramified H^3 of X with coefficients Q_l/Z_l(2) in the style of Colliot-Th\'el\`ene and Voisin. If k is separably closed, finite or…

We study the Fulton-Macpherson operational Chow rings of good moduli spaces of properly stable, smooth, Artin stacks. Such spaces are \'etale locally isomorphic to geometric invariant theory quotients of affine schemes, and are therefore…

In this paper we study the moduli stack ${\mathcal U}_{1,n}^{ns}$ of curves of arithmetic genus 1 with n marked points, forming a nonspecial divisor. In arXiv:1511.03797 this stack was realized as the quotient of an explicit scheme…

In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and it is endowed with a scheme structure. We introduce a relative version of the Krichever map using a fibration of Sato…

In this note we intend to look at the moduli stacks for global $G$-shtukas from a new perspective. We discuss a unifying interpretation of several moduli spaces (stacks) including moduli of global $G$-shtukas and (a variant of the) moduli…

Assuming everywhere good reduction we generalize the class number formula of Taelman to Drinfeld modules over arbitrary coefficient rings. In order to prove this formula we develop a theory of shtukas and their cohomology.

In this paper we classify isogeny classes of global $\mathsf{G}$-shtukas over a smooth projective curve $C/\mathbb{F}_q$ (or equivalently $\sigma$-conjugacy classes in $\mathsf{G}(\mathsf{F} \otimes_{\mathbb{F}_q} \overline{\mathbb{F}_q})$…

This is the first in a sequence of two articles investigating moduli stacks of global G-shtukas, which are function field analogs for Shimura varieties. Here G is a flat affine group scheme of finite type over a smooth projective curve, and…

We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…

For a reductive group $G$ over a discretely valued Henselian field $k$, using valuations of root datum and concave functions, the Bruhat--Tits theory defines an important class of open bounded subgroups of $G(k)$ which are essential objects…

We study moduli spaces of (possibly non-nodal) curves (C,p_1,\ldots,p_n) of arithmetic genus g with n smooth marked points, equipped with nonzero tangent vectors, such that ${\mathcal O}_C(p_1+\ldots+p_n)$ is ample and $H^1({\mathcal…

Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each…

We provide explicit equations for moduli spaces of Drinfeld shtukas over the projective line with $\Gamma(N)$, $\Gamma_1(N)$ and $\Gamma_0(N)$ level structures, where $N$ is an effective divisor on $\mathbb{P}^1$. If the degree of $N$ is…

This is the second in a sequence of articles, in which we explore moduli stacks of global G-shtukas, the function field analogs for Shimura varieties. Here G is a flat affine group scheme of finite type over a smooth projective curve C over…