Logarithmic geometry and algebraic stacks

DOI10.1016/j.ansens.2002.11.001zbMath1069.14022OpenAlexW2005595639MaRDI QIDQ3155496

Publication date: 17 January 2005

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_2003_4_36_5_747_0

zbMATH Keywords

Grothendieck topologies algebraic spaces sites fibred categories log structures étale topologies

Mathematics Subject Classification ID

Algebraic moduli problems, moduli of vector bundles (14D20) Fibered categories (18D30) Generalizations (algebraic spaces, stacks) (14A20) Schemes and morphisms (14A15) Local structure of morphisms in algebraic geometry: étale, flat, etc. (14B25)

Related Items

Stable pair, tropical, and log canonical compactifications of moduli spaces of del Pezzo surfaces, A general formalism for logarithmic structures, Integral morphisms and log blow-ups, KUMMER COVERINGS AND SPECIALISATION, Canonical Artin stacks over log smooth schemes, Kato-Nakayama spaces, infinite root stacks and the profinite homotopy type of log schemes, Boundedness of the space of stable logarithmic maps, Logarithmic good reduction of abelian varieties, Langlands correspondence for isocrystals and the existence of crystalline companions for curves, The log product formula, The Log Product Formula in Quantum K-theory, The monodromy pairing for logarithmic 1-motifs, Algebraic geometry in mixed characteristic, Towards logarithmic GLSM: the \(r\)-spin case, Genus 0 logarithmic and tropical fixed‐domain counts for Hirzebruch surfaces, A classification of modular compactifications of the space of pointed elliptic curves by Gorenstein curves, Moduli of parabolic sheaves on a polarized logarithmic scheme, The degeneration formula for stable log maps, Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces, A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves, A MODULI STACK OF TROPICAL CURVES, Logarithmic quasimaps, Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes, Splitting of Gromov–Witten invariants with toric gluing strata, Erratum: "Notes on algebraic log stack", On log flat descent, Toroidal orbifolds, destackification, and Kummer blowings up, Parabolic sheaves on logarithmic schemes, Universal log structures on semi-stable varieties, Tropical refined curve counting from higher genera and lambda classes, Non-Archimedean geometry of Artin fans, Decomposition of degenerate Gromov–Witten invariants, Logarithmically regular morphisms, Comparison theorems for Gromov-Witten invariants of smooth pairs and of degenerations, Birational invariance in logarithmic Gromov–Witten theory, Quantum (non-commutative) toric geometry: foundations, Twisted stable maps to tame Artin stacks, Logarithmic structures of Fontaine-Illusie. II: Logarithmic flat topology, A product formula for log Gromov-Witten invariants, The degeneration formula for logarithmic expanded degenerations, Dominant rational maps in the category of log schemes, Logarithmic Gromov-Witten invariants, On the conductor formula of Bloch, Toroidal crossings and logarithmic structures., Integral models for moduli spaces of \(G\)-torsors, Étale dévissage, descent and pushouts of stacks, Geometry of Chow quotients of Grassmannians, On relative and overconvergent de Rham-Witt cohomology for log schemes, Parabolic sheaves with real weights as sheaves on the Kato-Nakayama space, The circle quantum group and the infinite root stack of a curve, A non-Archimedean analogue of Teichmüller space and its tropicalization, Equivariant versal deformations of semistable curves, Stable logarithmic maps to Deligne-Faltings pairs I, Towards non–abelian 𝑝–adic Hodge theory in the good reduction case, The category of toric stacks, Notes on algebraic log stack, Skeletons and Fans of Logarithmic Structures, Quasisymmetric functions and the Chow ring of the stack of expanded pairs, Virtual normalization and virtual fundamental classes, Smoothing of semistable Fano varieties, \(\mathbb{A}^1\)-curves on log smooth varieties, On a logarithmic version of the derived McKay correspondence, The logarithmic cotangent complex, Relative log-symplectic structure on a semi-stable degeneration of moduli of Higgs bundles, A compactification of the space of maps from curves, Tangent curves to degenerating hypersurfaces, The higher-dimensional tropical vertex, Tropical compactification in log-regular varieties, From Pierre Deligne's secret garden: looking back at some of his letters, \(\mathbb A^1\)-connected varieties of rank one over nonclosed fields, Logarithmic étale cohomology. II.

Cites Work