On the S-fundamental group scheme
Adrian Langer
本文对定义在正特征的代数闭域上的簇引入了一个新的基本群方案，并利用它研究了C. Simpson的结果为阳性特征。我们还研究了这个群的性质，并证明了Lefschetz型定理。
We introduce a new fundamental group scheme for varieties defined over an algebraically closed field of positive characteristic and we use it to study generalization of some of C. Simpson's results to positive characteristic. We also study the properties of this group and we prove Lefschetz type theorems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this article, we study the log-scheme theoretic version of the Nori fundamental group scheme. Similar to the classical Nori fundamental group scheme, the log Nori fundamental group scheme classifies torsors on log flat topology. We also compute the nilpotent pro-p quotient of the log Nori fundamental group scheme with log at $\{0, 1, \infty\}$.
The Fundamental Group Scheme of a non Reduced Scheme
本文将基本群概型的定义推广到任意连通Dedekind概型上的非约化概形。然后比较了仿射格式的基本群格式和它的约化部分的基本群格式。
The tame fundamental group schemes of curves in positive characteristic
本文研究正特征代数闭域上光滑曲线的驯服基本群概形，发展余特化映射理论，证明其依赖曲线且可重构数值不变量。
Let $k$ be an algebraically closed field of characteristic $p > 3$. Let $X$ be an irreducible smooth projective surface over $k$. Fix an integer $n \geq 1$ and let ${\mathcal{H}{\it ilb}}_X^n$ be the Hilbert scheme parameterizing effective $0$-cycles of length $n$ on $X$. The aim of the present article is to find the $S$-fundamental group scheme and Nori's fundamental group scheme of the Hilbert scheme $\mathcal{H}{\it ilb}_X^n$.
In this note, we prove that the F-fundamental group scheme is birational invariant for smooth projective varieties. We prove that the F-fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. For elliptic curves, it turns out that the F-fundamental group scheme and the Nori fundamental group scheme coincides. We also consider an extension of the Nori fundamental group scheme in positive characteristic using semi-essentially finite vector bundles and prove that in this way, we do not get a non-trivial extension of the Nori fundamental group scheme for elliptic cur…
Notes On Fundamental Groupoid Schemes
本文研究了对应于特定向量丛Tannakian范畴的基本群胚概形，计算了各向异性圆锥、Klein瓶和阿贝尔簇的基本群胚概形，并通过表示探讨了它们之间的关系。
The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme
定义了任意（非空）基概型上约化群概型的代数基本群函子，并证明了该函子是正合的。
Let $k$ be an algebraically closed field. Let $C$ be an irreducible smooth projective curve over $k$. Let $E$ be a locally free sheaf on $C$ of rank $\geq 2$. Fix an integer $d \geq 2$. Let $\mathcal{Q}$ denote the Quot scheme parameterizing torsion quotients of $E$ of degree $d$. In this article we compute the $S$-fundamental group scheme of $\mathcal{Q}$.
Birational invariance of the $S$-fundamental group scheme
设$X$和$Y$是正特征代数闭域$k$上的非奇异投射簇.如果$X$和$Y$是双有理的，我们证明了它们的$S$ -基本群格式是同构的.
In this paper we describe the fundamental group-scheme of a proper variety fibered over an abelian variety with rationally connected fibers over an algebraically closed field. We use old and recent results for the Nori fundamental group-scheme, and of finite group-schemes in general to prove that the kernel of such a fibration is finite, and that the homotopy exact sequence holds in this case. As an application, we describe the fundamental group-schemes of certain proper varieties that are connected by curves or are related to them.
Some Further Remarks on the Local Fundamental Group Scheme
我们证明了局部基本群格式在特征p下满足Lefschetz-Bott定理，这些证明是Enriques-Severi -Zakki-Serre消灭定理和已知p-曲率事实的标准应用
On the fundamental group scheme of rationally chain connected varieties
设$k$是一个代数闭域. Chambert-Loir证明了$k$上正规有理链连通簇的顶点基本群是有限的.本文证明了$k$上正规有理链连通簇的基本群概型是有限的和无尾的.特别地，Fano簇的基本群概型是有限的且不稳定的。
Weak Density of the Fundamental Group Scheme
关于代数闭域上的$X$投射光滑，证明了若Nori的基本群概型是平凡的，则不存在非平凡的0次Nori半稳定丛，即Langer特别研究的群概型$π^S(X)$是平凡的.
On the S-fundamental group scheme II
S-基本群格式是对应于数值平坦向量丛的Tannaka范畴的群格式。本文利用行列式线丛证明了两个完全簇的乘积的S-基本群是它们的S-基本群的乘积。我们还计算了交换簇或具有平凡根基本群的簇的S-基本群概型和S-基本群概型的交换部分。
Finite group schemes as fundamental group schemes of smooth projective varieties
本文研究将有限群概形实现为光滑射影簇基本群概形的问题，通过贝尔蒂尼型结果、戈多-塞雷构造等方法，证明在无限完美域k上任意有限群概形G/k均可作为对应类型的基本群概形实现于特定维数的连通光滑射影簇。
Let $k$ be an algebraically closed field of characteristic $p > 3$. Let $A$ be an abelian surface over $k$. Fix an integer $n \geq 1$ such that $p \nmid n$ and let $K^{[n]}$ be the $n$-th Generalized Kummer Variety associated to $A$. In this article we aim to find the $S$-fundamental group scheme and Nori's fundamental group scheme of $K^{[n]}$.
Two small remarks on Nori fundamental group scheme
对于特征为$p>0$的完满域上的完备的、约化的、几何连通的$X$格式，本文分析了Nori的基本群格式的局部分解和非局部分解，并提出了群格式的分裂与几何的关系问题.我们还描述了范畴的函子对应的最大约化子群计划的列入。
A Simple Application of Enriques-Severi-Zariski-Serre to the Local Fundamental Group Scheme
证明了局部基本群格式满足Lefschetz-Bott-Grothendieck条件。
A smooth counterexample to Nori's conjecture on the fundamental group scheme
我们证明了Nori的基本群方案π（X，x）在特征为2的域上定义的亏格为2的光滑射影普通曲线X的基域扩张下不正确地基变换.
Some Remarks on the Local Fundamental Group Scheme
本文定义了由F-平凡向量丛定义的局部基本群方案，并给出了它基变的充要条件。
Let $k$ be an algebraically closed field of characteristic $p > 0$. Let $X$ be an irreducible smooth projective curve of genus $g$ over $k$. Fix an integer $n \geq 2$, and let $S^n(X)$ be the $n$-fold symmetric product of $X$. In this article we find the $S$-fundamental group scheme and Nori's fundamental group scheme of $S^n(X)$.
The action of the étale fundamental group scheme on the connected component of the essentially finite one
我们遵循Otabe [Ota15]最近的一篇论文中的模式，定义了一个作用的étale基本群计划$π^\text{et}(X)$的本地组件的本质有限基本群计划$π^{\mathrm{EF}}(X)$的Nori。当$X$是亏格$\geq 2$的曲线时，我们证明了相关表示是忠实的。
Abelianization of the F-divided fundamental group scheme
设$(X ,x_0)$是定义在代数闭域上的点光滑真簇. $(X ,x_0)$的Albanese态射从$X$的$F$ -划分的基本群方案的阿贝尔化到$X$的Albanese簇的$F$ -划分的基本群产生同态。我们证明了这个同态是具有有限核的满射。内核也被描述。
Desingulization of Quasi-smooth Derived Schemes and Virtual Fundamental Classes
证明拟光滑导出概形的去奇异化定理，并提出其虚拟基本类K理论积分与光滑概形上完美复形楔幂积分等价的猜想。
On an extension of Nori and local fundamental group schemes
本文探讨了Abelian簇的扩展Nori和局部基本群方案，分析了其birational不变性及在Albanese和étale映射下的行为。
Comparison of fundamental group schemes of a projective variety and an ample hypersurface
设$X$是定义在代数闭域上的光滑射影簇，$L$是$X$上的充裕线丛.证明了对完备线性系统$| L^{\otimes d}|$中$X$上的任意光滑超曲面$D$，只要$d$足够大且$\dim X \geq 3$，包含映射$D\hookrightarrow X$诱导基本群方案同构.如果$\dim X = 2$和$d$足够大，则基本群格式的诱导同态保持满射。我们给出一个例子，说明由光滑射影曲面中约化的充分曲线的包含映射导出的基本群格式的同态一般不是满射的。
Loops on schemes and the algebraic fundamental group
本文通过引入区间概形重新解释真概形的代数基本群，定义代数环路与同伦关系，并利用麦考利化和勒夫谢茨型结果建立主要结论。
On the bumpy fundamental group scheme
在这篇短文中，我们首先回顾了在已知的两种情形下：定义在域上和定义在Dedekind概型上的概型$X$的基本群概型的定义和构造。它对$X$上的所有有限（或准有限）fpqc torsor进行分类。当$X$被定义在任意维数的诺特正则模式$S$上时，我们不知道这样的对象是否可以被构造。这就是为什么我们引入一个新的类别，包含fpqc torsors，其对象是新拓扑的torsors。我们证明了这个新的类别是cofiltered从而产生一个基本群计划在$S$，说\textit{bumpy}，因为它可能不是平坦的一般。我们证明了当$S$是Dedekind格式时，它是平坦的，从而与\textit{classical}格式一致.
On Nori's Fundamental Group Scheme
我们确定了Nori的基本群方案到其顶点和局部的同态的核的表示范畴--商范畴。Pierre Deligne指出了本文第一版中的一个错误。我们深深地感谢他，特别是他给我们的启示的例子复制在备注2.4 2）。
Higgs bundles and fundamental group schemes
本文利用数值有效性概念证明数值平坦希格斯向量丛构成Tannaka范畴，引入希格斯基本群概形，并将其性质与陈类消失猜想联系起来。
Order 1 congruences of lines with smooth fundamental scheme
本文给出了一阶Cohen-Macaulay线的不可约同余的基本概型的概念.我们证明了这样的一个同余是由k-割线形成的基本计划的一个数字k，我们称之为割线指数的同余。如果基本概型X是PN中的光滑连通簇，则k =（N-1）/（c-1）（其中c是X的余维数），并且X配备有被k-2次虚拟超曲面切割的特殊切因子（准确地说，线性等价于被（k-2）次超曲面切割而不被切割的截面）。这在本文的主要定理中得到了解释。在此基础上，给出了光滑基本格式下已知的线的局部Cohen-Macaulay 1阶同余的完全分类。最后，我们注意到，根据Zak的分类Severi品种和低余维品种的Harthsorne猜想，这种分类是完整的。
We construct virtual fundamental classes on nested Hilbert schemes of points and curves in complex nonsingular projective surfaces. These classes recover the virtual classes of Seiberg-Witten theory as well as the (reduced) stable theory, and play a crucial role in the reduced Donaldson-Thomas theory of local-surface-threefolds that we study in [GSY17b] (arXiv:1807.05697). We show that certain integrals against the virtual fundamental classes of punctual nested Hilbert schemes are expressed as integrals over the products of the Hilbert scheme of points. We are able to find explicit formulas fo…
On base change of the fundamental group scheme
我们提供了所有素数$p$的例子，光滑的射影曲线在一个领域的特征$p$的基础变化的基本群计划失败。这与$F$ -平凡向量丛（即被弗罗贝尼乌斯态射的幂平凡化的丛）在（平凡）族中的行为密切相关。最后，我们研究的行为$F$ -平凡（不一定平凡）的家庭。
On the fundamental group schemes of certain quotient varieties
本文在$F$-divided和本质有限基本群概形的设定下，证明了Armstrong关于商空间基本群定理的类似结果。
Fundamental group schemes of globally F-regular varieties
该研究证明正特征代数闭域上连通正规整体F-正则射影簇的连通拟挠子覆盖塔稳定，其正则轨迹的Nori基本群概型有限且线性约化，有限性是Xu和Braun相关定理的正特征类比。
Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces
在[DKO]中，我们构造了曲面V上拓扑型m因子的希尔伯特方案的虚拟基本类$[[ Hilb^m_V ]]$，并使用这些类定义V的庞加莱不变量：（P^+_V，P^-_V）：H^2（V，Z）--> Λ^* H^1（V，Z）x Λ^* H^1（V，Z）Z）我们推测这个不变量与关于正则方向数据计算的完整的Seiberg-Witten不变量一致。本文证明了积分曲线$C \subset V$的存在性导致了某些虚基本类$[[Hilb^m_V ]]$之间的关系。Poincare不变量的对应关系可以看作是[OS]中基本关系的代数类比。
Vector bundles trivialized by proper morphisms and the fundamental group scheme
设X是定义在代数闭域k上的光滑射影簇。Nori在X上构造了一个向量丛范畴，称为本质有限向量丛，这让人想起基本群（特征为零）的表示范畴。事实上，这个范畴等价于控制所有有限扭子的亲有限群概型的表示范畴。我们证明了本质有限的向量丛与那些在被某些真满射拉回到X之后变得平凡的向量丛是一致的。
Let $R$ be a discrete valuation ring with fraction field $K$. Let $X$ be a proper and faithfully flat $R$-scheme, endowed with a section $x \in X(R)$, with connected and reduced generic fibre $X_η$. Let $f: Y \rightarrow X_η$ be a finite Nori-reduced $G$-torsor. In this paper we provide a useful criterion to extend $f: Y \rightarrow X_η$ to a torsor over $X$. Furthermore in the particular situation where $R$ is a complete discrete valuation ring of residue characteristic $p>0$ and $X\to \text{Spec}(R)$ is smooth we apply our criterion to prove that the natural morphism $ψ^{(p')}: π(X_η,x_η)^{(…
Vector bundles trivialized by proper morphisms and the fundamental group scheme, II
设$X$是代数闭域$k$上的投射光滑簇.设$f:Y\rightarrow X$是$k$ -簇的真满射.假设$f$是可分的，我们证明了与$X$上的向量丛$E$相关联的Tannakian范畴，使得$f^*E$是平凡的，等价于一个有限的代数群概型的表示范畴.在不存在可分性的情况下，我们给出了这个结论的一个反例。
Isomorphism of étale fundamental groups lifts to isomorphism of stratified fundamental group
本文证明光滑射影簇间的有限一般光滑态射若诱导 étale 基本群同构，则其诱导的分层基本群映射也是同构。
Let $S$ be a connected Dedekind scheme and $X$ be a proper smooth connected scheme over $S$ . Let $D$ a divisor with no multiplicity of $X$ such that the irreducible components of $D$ and as well their intersections are smooth over $S$. Now if we endow $X$ with the log structure associated with $D$ then the structure morphism from $X$ to $S$ is log-smooth. Let $x: S \to X$ be a $S$-point such that it doesn't intersect $D$. Then we prove that the maximal abelian quotient of the log Nori fundamental group scheme of $X$ fits in to an exact sequence of the form $0 \rightarrow (\mathbf{NS}^τ_{X/S,D…
The fundamental group of period domains over finite fields
确定了有限域上周期域的基本群。
Tempered fundamental group and metric graph of a Mumford curve
本文试图给出$p$ -adic光滑代数簇的调和基本群（它是p-adic世界中复代数簇的拓扑基本群的一种模拟）的一些一般性结果。主要结果表明，人们可以从Mumford曲线的调和基本群恢复Mumford曲线的稳定模型的图的度量结构。我们还将证明双有理不变性，代数封闭的扩展和Kuenneth公式的回火基本群的不变性。我们将描述交换阿贝尔簇的调和基本群，并将曲线的调和基本群与其雅可比簇的调和基本群联系起来。
Let $X$ be any scheme defined over a Dedekind scheme $S$ with a given section $x\in X(S)$. We prove the existence of a pro-finite $S$-group scheme $\aleph(X,x)$ and a universal $\aleph(X,x)$-torsor dominating all the pro-finite pointed torsors over $X$. Though $\aleph(X,x)$ may not be unique in general it still can provide useful information in order to better understand $X$. In a similar way we prove the existence of a pro-algebraic $S$-group scheme $\aleph^{\rm alg}(X,x)$ and a $\aleph^{\rm alg}(X,x)$-torsor dominating all the pro-algebraic and affine pointed torsors over $X$. The case where…
Finiteness of fundamental groups
我们证明了低维log Fano对光滑轨迹的基本群的有限性将意味着klt奇点的局部基本群的有限性。作为应用，我们证明了三维klt奇点的局部基本群和具有典型奇点的三维Fano簇的光滑轨迹的基本群总是有限的.
Finiteness of algebraic fundamental groups
证明了任意klt奇点的代数局部基本群以及任意log Fano簇的光滑轨迹的代数基本群都是有限的.
Binoid schemes generalise monoid schemes, which in turn enable us to generalise toric varieties. Let $X$ be a binoid scheme. The aim of this paper is to calculate the topological fundamental group of $KX$, where $K=\mathbb{C}$ or $\mathbb{R}$. For the latter, we will give an explicit way of calculating the fundamental group using methods from 2-category theory. Indeed, we will calculate the more general fundamental groupoid. As a specialisation, we will also look at the Stanley Reisner Rings. Our method simplifies in this case, allowing us to describe the fundamental groupoid in terms of the s…
$D$-local algebraic fundamental groups of germs of normal complex analytic singularities
本文将正规复解析奇点的局部代数基本群的概念推广到某些称为$D$ -局部代数基本群的投射有限群上，证明了$D$ -局部代数基本群的Lefshetz型定理.例如，该定理给出了某类四维奇点的局部代数基本群的有限性，并将对三维纯对数终端奇点的分类有用。
The Künneth Formula Of Fundamental Group Schemes
针对proper态射，给出Tannakian基本群概形同伦序列正合的统一判据，进而得到两个proper连通概形乘积的基本群概形Künneth公式的等价条件，并应用于多种基本群概形。
Every finite flat finitely presented group scheme G of square free order over a scheme S can be written as an extension of a finite etale S-group scheme G" by a commutative finite flat finitely presented S-group scheme G' that is a direct sum of group schemes of prime order. Such an extension splits over a finite etale surjective base change.
The abelian fundamental group with modulus in mixed characteristic
本文在混合特征下定义了带模的交换基本群，并证明了严格半稳定概形上限制到足够大次数超曲面诱导交换基本群同构的Lefschetz型定理。
We prove a conjecture of Kollár stating that the local fundamental group of a klt singularity $x$ is finite. In fact, we prove a stronger statement, namely that the fundamental group of the smooth locus of a neighbourhood of $x$ is finite. We call this the regional fundamental group. As the proof goes via a local-to-global induction, we simultaneously confirm finiteness of the orbifold fundamental group of the smooth locus of a weakly Fano pair.
The fundamental group is not a derived invariant
我们证明了基本群在光滑射影簇的导出等价下不是不变的。
Finiteness of étale fundamental groups by reduction modulo $p$
我们引入了一种展开技术，通过特征$p$方法推导出复簇的代数基本群的有限性结果，并将其应用于最近证明的一个利用双有理几何在特征$0$中局部基本群的有限性结果.
The Fundamental Group of an Algebraic Stack
定义了代数栈的基本群的概念，证明了复数上的栈的基本群与相应的解析轨道的比较定理，证明了这个概念与Oda用单纯形方案定义的概念是一致的，最后证明了涉及这些群的一些短正合列.
Picard Groups and Class Groups of Monoid Schemes
定义并研究了么半群概型的Picard群和正规么半群概型的类群。为了做到这一点，我们发展了一些理想的理论（点交换）诺特幺半群，包括准素分解和离散赋值。一个幺半群的正规化结果是一个幺半群方案，但并不总是一个幺半群。
On the algebraic fundamental group of smooth varieties in characteristic $p>0$
定义了一个类似于复流形的拓扑基本群的前代数完备的特征$p>0$。
Coverings in p-adic analytic geometry and log coverings II: Cospecialization of the p'-tempered fundamental group in higher dimensions
本文构造了具有多稳定约化的光滑态射的纤维的回火基本群的（p '）版本之间的余特化同态（回火基本群是p进世界中复代数簇的拓扑基本群的一种模拟）.我们在另一篇论文中研究了曲线族的问题。为了构造它们，我们首先用对数结构的约化描述具有多稳定约化的光滑真簇的亲（p '）调和基本群，从而定义对数多稳定簇的调和基本群.
Abelianisation of orthogonal groups and the fundamental group of modular varieties
研究了不定二次型的整正交群的换位子群。我们表明，该交换子的指数是2的许多群体中发生的模空间在代数几何，特别是模的K3表面的建设。给出了模形式和计算某些模空间的基本群的应用。
In this paper, we give a set of generators and relations of the fundamental group of the non-singular locus of Lauricella's hypergeometric functions
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。