scholarly journals Toroidal compactifications of integral models of Shimura varieties of Hodge type

2019 ◽  
Vol 52 (2) ◽  
pp. 393-514 ◽  
Author(s):  
Keerthi MADAPUSI PERA
Keyword(s):  
Shimura Varieties ◽  
Toroidal Compactifications

scholarly journals Chern classes of automorphic vector bundles, II

2019 ◽  
Vol Volume 3 ◽  
Author(s):  
Hélène Esnault ◽  
Michel Harris
Keyword(s):  
Galois Group ◽  
Vector Bundles ◽  
Shimura Varieties ◽  
Chern Classes ◽  
Toroidal Compactifications ◽  
Canonical Extensions

We prove that the $\ell$-adic Chern classes of canonical extensions of automorphic vector bundles, over toroidal compactifications of Shimura varieties of Hodge type over $\bar{ \mathbb{Q}}_p$, descend to classes in the $\ell$-adic cohomology of the minimal compactifications. These are invariant under the Galois group of the $p$-adic field above which the variety and the bundle are defined. Comment: 28 pages

scholarly journals Special cycles on toroidal compactifications of orthogonal Shimura varieties

2021 ◽  
Author(s):  
Jan Hendrik Bruinier ◽  
Shaul Zemel
Keyword(s):  
Shimura Varieties ◽  
Green Functions ◽  
Toroidal Compactifications ◽  
Generating Series ◽  
Automorphic Green Functions

AbstractWe determine the behavior of automorphic Green functions along the boundary components of toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define boundary components of special divisors and prove that the generating series of the resulting special divisors on a toroidal compactification is modular.

scholarly journals Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties

2018 ◽  
Vol 2020 (13) ◽  
pp. 3902-3926
Author(s):  
Réda Boumasmoud ◽  
Ernest Hunter Brooks ◽  
Dimitar P Jetchev
Keyword(s):  
Vertical Distribution ◽  
Three Dimensional ◽  
Complex Multiplication ◽  
Horizontal Distribution ◽  
Unitary Groups ◽  
Shimura Varieties ◽  
Heegner Points ◽  
Universal Norm

Abstract We consider cycles on three-dimensional Shimura varieties attached to unitary groups, defined over extensions of a complex multiplication (CM) field $E$, which appear in the context of the conjectures of Gan et al. [6]. We establish a vertical distribution relation for these cycles over an anticyclotomic extension of $E$, complementing the horizontal distribution relation of [8], and use this to define a family of norm-compatible cycles over these fields, thus obtaining a universal norm construction similar to the Heegner $\Lambda $-module constructed from Heegner points.

scholarly journals KLT factorization of winding string amplitudes

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Jaume Gomis ◽  
Ziqi Yan ◽  
Matthew Yu
Keyword(s):  
Scattering Amplitudes ◽  
Open String ◽  
Closed String ◽  
Open Strings ◽  
Toroidal Compactifications ◽  
Quantum Numbers ◽  
String Amplitudes

Abstract We uncover a Kawai-Lewellen-Tye (KLT)-type factorization of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The winding and momentum closed string quantum numbers map respectively to the integer and fractional winding quantum numbers of open strings ending on a D-brane array localized in the compactified directions. The closed string amplitudes factorize into products of open string scattering amplitudes with the open strings ending on a D-brane configuration determined by closed string data.

scholarly journals On a conjecture of Pappas and Rapoport about the standard local model for GL_d

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinakar Muthiah ◽  
Alex Weekes ◽  
Oded Yacobi
Keyword(s):  
Type A ◽  
Positive Answer ◽  
Local Model ◽  
Schubert Varieties ◽  
Shimura Varieties ◽  
Local Models ◽  
Full Generality ◽  
Frobenius Splitting ◽  
Affine Grassmannians ◽  
Main Ideas

AbstractIn their study of local models of Shimura varieties for totally ramified extensions, Pappas and Rapoport posed a conjecture about the reducedness of a certain subscheme of {n\times n} matrices. We give a positive answer to their conjecture in full generality. Our main ideas follow naturally from two of our previous works. The first is our proof of a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman on the equations defining type A affine Grassmannians. The second is the work of the first two authors and Kamnitzer on affine Grassmannian slices and their reduced scheme structure. We also present a version of our argument that is almost completely elementary: the only non-elementary ingredient is the Frobenius splitting of Schubert varieties.

Sign in / Sign up

Export Citation Format

Share Document