Finiteness of algebraic fundamental groups

Abstract

We show that the algebraic local fundamental group of any klt singularity as well as the algebraic fundamental group of the smooth locus of any log Fano variety are finite.

6 pages, final version

References in corpus (3)

• New examples of terminal and log canonical singularities
• ACC for log canonical thresholds
• Etale covers of Kawamata log terminal spaces and their smooth loci

Cited by in corpus (47)

• Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties
• The dual complex of Calabi--Yau pairs
• Stability of Valuations and Kollár Components
• ACC for minimal log discrepancies of exceptional singularities
• Uniform K-stability and plt blowups of log Fano pairs
• K-stability of cubic threefolds
• Fundamental groups of $F$-regular singularities via $F$-signature
• The normalized volume of a singularity is lower semicontinuous
• On the geometry of thin exceptional sets in Manin's Conjecture
• Finite torsors over strongly $F$-regular singularities
• Finiteness of fundamental groups
• The local fundamental group of a Kawamata log terminal singularity is finite
• Nonvanishing for threefolds in characteristic $p>5$
• The Jordan property for local fundamental groups
• Uniqueness of the minimizer of the normalized volume function
• Minimizing normalized volumes of valuations
• Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups
• Stability of Valuations: Higher Rational Rank
• Étale fundamental groups of strongly $F$-regular schemes
• Finiteness of étale fundamental groups by reduction modulo $p$
• A characterization of finite quotients of Abelian varieties
• Rational points on log Fano threefolds over a finite field
• $F$-signature under birational morphisms
• Manin's Conjecture and the Fujita invariant of finite covers
• Relative MMP without Q-factoriality
• Kawamata log terminal singularities of full rank
• A Minimizing Valuation is Quasi-monomial
• On divisors computing MLD's and LCT's
• Complements and coregularity of Fano varieties
• Étale Covers and Local Algebraic Fundamental Groups
• Reductive quotients of klt singularities
• A geometric characterization of toric singularities
• On boundedness of singularities and minimal log discrepancies of Kollár components, II
• Interaction Between Singularity Theory and the Minimal Model Program
• Tame fundamental groups of pure pairs and Abhyankar's lemma
• Uniformisation of higher-dimensional minimal varieties
• Etale covers of Kawamata log terminal spaces and their smooth loci
• On the semi-continuity problem of normalized volumes of singularities
• Symmetries of Fano varieties
• On exceptional sets in Manin's Conjecture
• Stable degeneration of families of klt singularities with constant local volume
• Étale coverings in codimension 1 with applications to Mori Dream Spaces
• On termination of flips and fundamental groups
• Fundamental group of log terminal T-varieties
• Infinitesimal structure of log canonical thresholds
• Zero cycles on rationally connected varieties over Laurent fields
• On the local étale fundamental group of KLT threefold singularities