From sum of two squares to arithmetic Siegel–Weil formulas

DOI10.1090/bull/1786arXiv2110.07457OpenAlexW3206007716MaRDI QIDQ6039995

Chao Li

Publication date: 24 May 2023

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.07457

zbMATH Keywords

Shimura varietiesSiegel-Weil formulasinner product formulas

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Theta series; Weil representation; theta correspondences (11F27) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Algebraic cycles (14C25)

Cites Work

• Integral canonical models for Spin Shimura varieties
• IMPROPER INTERSECTIONS OF KUDLA–RAPOPORT DIVISORS AND EISENSTEIN SERIES
• Quadratic Forms and Automorphic Forms
• Modular Forms and Special Cycles on Shimura Curves. (AM-161)
• Theta dichotomy for unitary groups
• The Modularity of Special Cycles on Orthogonal Shimura Varieties over Totally Real Fields under the Beilinson–Bloch Conjecture
• Kudla–Rapoport cycles and derivatives of local densities
• Some cases of Kudla’s modularity conjecture for unitary Shimura varieties
• The Kudla-Rapoport conjecture at a ramified prime for 𝑈(1,1)
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• Arithmetic theta lifting and \(L\)-derivatives for unitary groups. I
• Arithmetic theta lifting and \(L\)-derivatives for unitary groups. II
• On the supersingular locus of the \(\mathrm{GU}(2,2)\) Shimura variety
• Special cycles on unitary Shimura varieties. II: Global theory
• The regularized Siegel-Weil formula (the second term identity) and the Rallis inner product formula
• Intersections of arithmetic Hirzebruch-Zagier cycles
• Special cycles on unitary Shimura varieties. I: Unramified local theory
• The supersingular locus of the Shimura variety of \(\text{GU}(1,n-1)\). II
• Algebraic cycles on Shimura varieties of orthogonal type
• On the intersection of modular correspondences
• Gross-Zagier formula for \(\text{GL}_ 2\).
• A reformulation of the Siegel series and intersection numbers
• Height pairings for algebraic cycles
• On the local theta-correspondence
• The theta correspondence and harmonic forms. I
• On canonical and quasi-canonical liftings
• Heegner points and derivatives of \(L\)-series
• K-theory, arithmetic and geometry. Seminar, Moscow University, 1984-1986
• Heegner points and derivatives of \(L\)-series. II
• Arithmetic intersection theory
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• Coxeter orbits and eigenspaces of Frobenius
• Central derivatives of Eisenstein series and height pairings
• Local zeta functions on Hermitian forms and its application to local densities
• A regularized Siegel-Weil formula: The first term identity
• On the motive of a reductive group
• Some modular varieties of low dimension
• Height pairings on Shimura curves and \(p\)-adic uniformization
• Shtukas and the Taylor expansion of \(L\)-functions
• Faltings heights of abelian varieties with complex multiplication
• Arithmetic Siegel-Weil formula on \(X_{0}(N)\)
• Arithmetic theta lifts and the arithmetic Gan-Gross-Prasad conjecture for unitary groups
• Shtukas and the Taylor expansion of \(L\)-functions. II
• Green forms and the arithmetic Siegel-Weil formula
• The Gross-Kohnen-Zagier theorem in higher dimensions
• Linear forms, algebraic cycles, and derivatives of \(L\)-series
• Weil representation and arithmetic fundamental lemma
• Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series
• Chow groups and \(L\)-derivatives of automorphic motives for unitary groups
• Symmetric power functoriality for holomorphic modular forms. II.
• Remarks on generating series for special cycles on orthogonal Shimura varieties
• Special cycles on unitary Shimura varieties with minuscule parahoric level structure
• An explicit formula for the Siegel series of a quadratic form over a non-Archimedean local field
• On the arithmetic Siegel-Weil formula for GSpin Shimura varieties
• Special cycles on toroidal compactifications of orthogonal Shimura varieties
• Generating series of a new class of orthogonal Shimura varieties
• Theta correspondence for almost unramified representations of unitary groups
• \(L\)-functions and theta correspondence for classical groups
• Linear invariance of intersections on unitary Rapoport-Zink spaces
• The geometric theta correspondence for Hilbert modular surfaces
• Formal degrees and local theta correspondence
• Sur la formule de Siegel dans la théorie des groupes classiques
• Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables
• Borcherds products and arithmetic intersection theory on Hilbert modular surfaces
• Über die analytische Theorie der quadratischen Formen
• Über die analytische Theorie der quadratischen Formen. II
• Über die analytische Theorie der quadratischen Formen. III
• Indefinite quadratische Formen und Funktionentheorie. I
• Indefinite quadratische Formen und Funktionentheorie. II
• Cycles on Siegel threefolds and derivatives of Eisenstein series
• Intersections of special cycles on the Shimura variety for
• The Geometric and Arithmetic Volume of Shimura Varieties of Orthogonal Type
• Algebraic cycles and values of L-functions.
• Elliptic Modular Forms and Their Applications
• On two arithmetic theta lifts
• Regularized theta lifts for orthogonal groups over totally real fields
• Chow groups andL-derivatives of automorphic motives for unitary groups, II.
• COHOMOLOGICAL ARITHMETIC CHOW RINGS
• KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES
• The Gross–Kohnen–Zagier theorem over totally real fields
• A note on local densities of quadratic forms
• On the Weil-Siegel formula II.
• An Explicit Formula for Siegel Series
• Arithmetic Hirzebruch Zagier cycles
• Period Spaces for "p"-divisible Groups (AM-141)
• Spherical functions on U(2n)/ (U(n) × U(n)) and hermitian Siegel series
• Incoherent Definite Spaces and Shimura Varieties
• On derivatives of Siegel–Eisenstein series over global function fields
• Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields
• Modularity of special cycles on unitary Shimura varieties over CM-fields
• Unitary cycles on Shimura curves and the Shimura lift II
• Endoscopic Classification of representations of Quasi-Split Unitary Groups

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