Special cycles on unitary Shimura varieties. I: Unramified local theory

DOI10.1007/s00222-010-0298-zzbMath1229.14020arXiv0804.0600OpenAlexW2002457466WikidataQ56700329 ScholiaQ56700329MaRDI QIDQ634647

Michael Rapoport, Stephen S. Kudla

Publication date: 16 August 2011

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.0600

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Formal groups, (p)-divisible groups (14L05)

Related Items (38)

Algebraic number theory. Abstracts from the workshop held June 19--25, 2011. ⋮ An arithmetic transfer identity ⋮ Local constancy of intersection numbers ⋮ On the arithmetic Siegel-Weil formula for GSpin Shimura varieties ⋮ On the regularity of special difference divisors ⋮ Serre's tensor construction and moduli of abelian schemes ⋮ On the arithmetic fundamental lemma through Lie algebras ⋮ Intersections of arithmetic Hirzebruch-Zagier cycles ⋮ From sum of two squares to arithmetic Siegel–Weil formulas ⋮ Special cycles on unitary Shimura curves at ramified primes ⋮ Remarks on the arithmetic fundamental lemma ⋮ A proof of the Kudla-Rapoport conjecture for Krämer models ⋮ On arithmetic fundamental lemmas ⋮ Kudla–Rapoport conjecture for Krämer models ⋮ Higher Siegel-Weil formula for unitary groups: the non-singular terms ⋮ Special cycles on the basic locus of unitary Shimura varieties at ramified primes ⋮ Basic loci of Coxeter type with arbitrary parahoric level ⋮ The supersingular locus of the Shimura variety of \(\text{GU}(1,n-1)\). II ⋮ IMPROPER INTERSECTIONS OF KUDLA–RAPOPORT DIVISORS AND EISENSTEIN SERIES ⋮ Regular formal moduli spaces and arithmetic transfer conjectures ⋮ Complex multiplication cycles and Kudla-Rapoport divisors ⋮ Arithmetic diagonal cycles on unitary Shimura varieties ⋮ The supersingular locus of the Shimura variety for \(\mathrm{GU}(1, n-1)\) over a ramified prime ⋮ On the lifting of Hilbert cusp forms to Hilbert-Hermitian cusp forms ⋮ An alternative description of the Drinfeld \(p\)-adic half-plane ⋮ Unitary cycles on Shimura curves and the Shimura lift II ⋮ The arithmetic fundamental lemma: an update ⋮ Fully Hodge-Newton decomposable Shimura varieties ⋮ Weil representation and arithmetic fundamental lemma ⋮ FINE DELIGNE–LUSZTIG VARIETIES AND ARITHMETIC FUNDAMENTAL LEMMAS ⋮ Heights of Kudla-Rapoport divisors and derivatives of \(L\)-functions ⋮ Chow groups andL-derivatives of automorphic motives for unitary groups, II. ⋮ Chow groups and \(L\)-derivatives of automorphic motives for unitary groups ⋮ Special cycles on unitary Shimura varieties with minuscule parahoric level structure ⋮ Linear invariance of intersections on unitary Rapoport-Zink spaces ⋮ On the arithmetic fundamental lemma in the minuscule case ⋮ Kudla–Rapoport cycles and derivatives of local densities ⋮ RELATIVE UNITARY RZ-SPACES AND THE ARITHMETIC FUNDAMENTAL LEMMA

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