Cycles on Siegel threefolds and derivatives of Eisenstein series

DOI10.1016/S0012-9593(00)01051-XzbMath1045.11044OpenAlexW2593456569MaRDI QIDQ2703175

Stephen S. Kudla, Michael Rapoport

Publication date: 18 June 2002

Published in: Annales Scientifiques de l'à cole Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_2000_4_33_5_695_0

zbMATH Keywords

algebraic cyclesmetaplectic groupintersection multiplicities of the cycles at isolated pointsSiegel modular variety of genus twospecial endomorphismsspecial values of derivatives of certain Eisenstein series

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Arithmetic aspects of modular and Shimura varieties (11G18) Heights (11G50) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Modular and Shimura varieties (14G35)

Related Items (21)

The derivative of an incoherent Eisenstein series ⋮ Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields ⋮ On the arithmetic Siegel-Weil formula for GSpin Shimura varieties ⋮ Reductions of abelian surfaces over global function fields ⋮ A geometric Jacquet-Langlands correspondence for paramodular Siegel threefolds ⋮ Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences ⋮ Intersections of arithmetic Hirzebruch-Zagier cycles ⋮ From sum of two squares to arithmetic Siegel–Weil formulas ⋮ On recursive properties of certain \(p\)-adic Whittaker functions ⋮ Special cycles on unitary Shimura varieties. I: Unramified local theory ⋮ Height pairings on orthogonal Shimura varieties ⋮ Rapoport–Zink spaces for spinor groups ⋮ Cell decomposition of some unitary group Rapoport-Zink spaces ⋮ Twisted Hilbert modular surfaces, arithmetic intersections and the Jacquet-Langlands correspondence ⋮ Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series ⋮ Incoherent Definite Spaces and Shimura Varieties ⋮ On the Bruhat-Tits stratification of a quaternionic unitary Rapoport-Zink space ⋮ On supersingular loci of Shimura varieties for quaternionic unitary groups of degree 2 ⋮ A reformulation of the Siegel series and intersection numbers ⋮ Affine Deligne-Lusztig varieties and the action of 𝐽 ⋮ Kudla–Rapoport cycles and derivatives of local densities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algebraic cycles on Shimura varieties of orthogonal type
• On the intersection of modular correspondences
• Class numbers of positive definite ternary quaternion Hermitian forms
• Fourier coefficients of Eisenstein series of degree 3
• Tamagawa numbers
• Existence of certain canonical models
• Central derivatives of Eisenstein series and height pairings
• An explicit formula for local densities of quadratic forms
• Height pairings on Shimura curves and \(p\)-adic uniformization
• On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms
• Which abelian surfaces are products of elliptic curves?
• A computation of the gamma matrix of a family of \(p\)-adic zeta integrals
• Algèbre locale. Multiplicités. Cours au Collège de France, 1957-1958, rédigé par Pierre Gabriel. 2e ed.
• La conjecture de Weil pour les surfaces K3
• Arithmetic of alternating forms and quaternion hermitian forms
• Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables
• A note on local densities of quadratic forms
• Points on Some Shimura Varieties Over Finite Fields
• On the reduction of the Hilbert-Blumenthal-moduli schem with Г0 (p)-level structure
• Arithmetic Hirzebruch Zagier cycles
• Travaux de Shimura

This page was built for publication: Cycles on Siegel threefolds and derivatives of Eisenstein series