On Moduli Stacks of G-bundles over a Curve

2010 ◽  
pp. 155-163 ◽  
Author(s):  
Norbert Hoffmann
Keyword(s):  
Moduli Stacks

scholarly journals Kac Polynomials for Canonical Algebras

2017 ◽  
Vol 2019 (13) ◽  
pp. 3981-4003
Author(s):  
Pierre-Guy Plamondon ◽  
Olivier Schiffmann
Keyword(s):  
Finite Field ◽  
Dimension Vector ◽  
Indecomposable Representations ◽  
Moduli Stacks ◽  
Fixed Dimension ◽  
Canonical Algebra

Abstract We prove that the number of geometrically indecomposable representations of fixed dimension vector $\mathbf{d}$ of a canonical algebra $C$ defined over a finite field $\mathbb{F}_q$ is given by a polynomial in $q$ (depending on $C$ and $\mathbf{d}$). We prove a similar result for squid algebras. Finally, we express the volume of the moduli stacks of representations of these algebras of a fixed dimension vector in terms of the corresponding Kac polynomials.

scholarly journals Uniformizing the Moduli Stacks of Global G-Shtukas

2019 ◽  
Author(s):  
E Arasteh Rad ◽  
Urs Hartl
Keyword(s):  
Finite Type ◽  
Moduli Spaces ◽  
Function Field ◽  
Group Scheme ◽  
Base Change ◽  
Generic Fiber ◽  
Smooth Projective Curve ◽  
Langlands Program ◽  
Moduli Stacks ◽  
Divisible Groups

Abstract This is the 2nd in a sequence of articles, in which we explore moduli stacks of global $\mathfrak{G}$-shtukas, the function field analogs for Shimura varieties. Here $\mathfrak{G}$ is a flat affine group scheme of finite type over a smooth projective curve $C$ over a finite field. Global $\mathfrak{G}$-shtukas are generalizations of Drinfeld shtukas and analogs of abelian varieties with additional structure. We prove that the moduli stacks of global $\mathfrak{G}$-shtukas are algebraic Deligne–Mumford stacks separated and locally of finite type. They generalize various moduli spaces used by different authors to prove instances of the Langlands program over function fields. In the 1st article we explained the relation between global $\mathfrak{G}$-shtukas and local ${{\mathbb{P}}}$-shtukas, which are the function field analogs of $p$-divisible groups. Here ${{\mathbb{P}}}$ is the base change of $\mathfrak{G}$ to the complete local ring at a point of $C$. When ${{\mathbb{P}}}$ is smooth with connected reductive generic fiber we proved the existence of Rapoport–Zink spaces for local ${{\mathbb{P}}}$-shtukas. In the present article we use these spaces to (partly) uniformize the moduli stacks of global $\mathfrak{G}$-shtukas for smooth $\mathfrak{G}$ with connected fibers and reductive generic fiber. This is our main result. It has applications to the analog of the Langlands–Rapoport conjecture for our moduli stacks.

scholarly journals Moduli of Bridgeland semistable objects on 3-folds and Donaldson–Thomas invariants

2019 ◽  
Vol 2019 (747) ◽  
pp. 175-219 ◽  
Author(s):  
Dulip Piyaratne ◽  
Yukinobu Toda
Keyword(s):  
Finite Type ◽  
Equivalent Form ◽  
Stability Conditions ◽  
Weak Stability ◽  
Algebraic Stacks ◽  
Moduli Stacks ◽  
Étale Quotients

Abstract In this paper we show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are quasi-proper algebraic stacks of finite type if they satisfy the Bogomolov–Gieseker (BG for short) inequality conjecture proposed by Bayer, Macrì and the second author. The key ingredients are the equivalent form of the BG inequality conjecture and its generalization to arbitrary very weak stability conditions. This result is applied to define Donaldson–Thomas invariants counting Bridgeland semistable objects on smooth projective Calabi–Yau 3-folds satisfying the BG inequality conjecture, for example on étale quotients of abelian 3-folds.

Local models for the moduli stacks of global $\mathfrak{G}$-shtukas

2019 ◽  
Vol 26 (2) ◽  
pp. 323-364 ◽  
Author(s):  
Esmail Arasteh Rad ◽  
Somayeh Habibi
Keyword(s):  
Local Models ◽  
Moduli Stacks

scholarly journals The Teichmüller and Riemann moduli stacks

2019 ◽  
Vol 6 ◽  
pp. 879-945
Author(s):  
Laurent Meersseman
Keyword(s):  
Moduli Stacks
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