Heights on stacks and a generalized Batyrev–Manin–Malle conjecture

DOI10.1017/fms.2023.5OpenAlexW3175144211WikidataQ123147716 ScholiaQ123147716MaRDI QIDQ5880156

Jordan S. Ellenberg, David Zureick-Brown, Matthew Satriano

Publication date: 7 March 2023

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.11340

Mathematics Subject Classification ID

Rational points (14G05) Varieties over global fields (11G35) Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Global ground fields in algebraic geometry (14G25) Stacks and moduli problems (14D23)

Related Items

The moduli space of \(G\)-algebras ⋮ Torsors for finite group schemes of bounded height ⋮ The scheme of monogenic generators. II: Local monogenicity and twists ⋮ Open problems in the wild McKay correspondence and related fields ⋮ An arithmetic valuative criterion for proper maps of tame algebraic stacks ⋮ Counting elliptic curves with prescribed level structures over number fields ⋮ Counting Drinfeld modules with prescribed local conditions ⋮ Problems in arithmetic topology

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algebraic points of bounded height on the projective line
• Counting algebraic points of bounded height on projective spaces
• The \(p\)-rank stratification of Artin-Schreier curves
• Noetherian approximation of algebraic spaces and stacks
• Quotients by groupoids
• Freedom and accumulation
• Intersection theory on algebraic stacks and on their moduli spaces
• Torsion points on elliptic curves over function fields and a theorem of Igusa
• Northcott's theorem on heights. I: A general estimate
• Level structures on abelian varieties, Kodaira dimensions, and Lang's conjecture
• Heights and Tamagawa measures on Fano varieties
• Beyond heights: slopes and distribution of rational points
• The number of \(D_4\)-fields ordered by conductor
• Artin-Schreier root stacks
• Statistics of the first Galois cohomology group: a refinement of Malle's conjecture
• Moduli spaces of rational curves on Fano threefolds
• Weighted greatest common divisors and weighted heights
• Vector bundles on the moduli stack of elliptic curves
• Rings of modular forms and a splitting of \(\mathrm{TMF}_0(7)\)
• There is no degree map for 0-cycles on Artin stacks
• Slicing the stars: counting algebraic numbers, integers, and units by degree and height
• Algebraic spaces
• Rational points of rationally simply connected varieties over global function fields
• Weak approximation for Fano complete intersections in positive characteristic
• Brauer groups and quotient stacks
• Zariski decompositions of numerical cycle classes
• Algebraic points, non-anticanonical heights and the Severi problem on toric varieties
• A construction of polynomials with squarefree discriminants
• Existence and properties of geometric quotients
• Courbes elliptiques: Formulaire
• Smooth toric Deligne-Mumford stacks
• The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields
• Northcott's theorem on heights II. The quadratic case
• Counting algebraic numbers with large height II
• Using stacks to impose tangency conditions on curves
• Mass Formulas for Local Galois Representations and Quotient Singularities. I: A Comparison of Counting Functions
• Counting Algebraic Numbers with Large Height I
• The Arithmetic of Elliptic Curves
• Counting points of fixed degree and bounded height
• ON COVERINGS OF DELIGNE–MUMFORD STACKS AND SURJECTIVITY OF THE BRAUER MAP
• A “Bottom Up” Characterization of Smooth Deligne–Mumford Stacks
• Modular invariants and isogenies
• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• Counting points of fixed degree and given height over function fields
• Stacks Project Expository Collection
• The shapes of Galois quartic fields
• Counting elliptic curves with an isogeny of degree three
• Campana points, Vojta’s conjecture, and level structures on semistable abelian varieties
• The shapes of pure cubic fields
• Level structures on abelian varieties and Vojta’s conjecture
• Mass Formulae for Extensions of Local Fields, and Conjectures on the Density of Number Field Discriminants
• ARITHMETIC MODULI OF GENERALIZED ELLIPTIC CURVES
• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point
• Toric stacks I: The theory of stacky fans