scholarly journals COMPACTIFICATIONS OF PEL-TYPE SHIMURA VARIETIES IN RAMIFIED CHARACTERISTICS

2016 ◽  
Vol 4 ◽  
Author(s):  
KAI-WEN LAN
Keyword(s):  
Shimura Varieties ◽  
Reduction Theory ◽  
Good Reduction ◽  
Treat All

We show that, by taking normalizations over certain auxiliary good reduction integral models, one obtains integral models of toroidal and minimal compactifications of PEL-type Shimura varieties which enjoy many features of the good reduction theory studied as in the earlier works of Faltings and Chai’s and the author’s. We treat all PEL-type cases uniformly, with no assumption on the level, ramifications, and residue characteristics involved.

scholarly journals RAPOPORT–ZINK UNIFORMIZATION OF HODGE-TYPE SHIMURA VARIETIES

2018 ◽  
Vol 6 ◽  
Author(s):  
WANSU KIM
Keyword(s):  
Shimura Varieties ◽  
Good Reduction ◽  
Canonical Models

We show that the integral canonical models of Hodge-type Shimura varieties at odd good reduction primes admits ‘$p$-adic uniformization’ by Rapoport–Zink spaces of Hodge type constructed in Kim [Forum Math. Sigma6(2018) e8, 110 MR 3812116].

scholarly journals Integral canonical models for Spin Shimura varieties

2015 ◽  
Vol 152 (4) ◽  
pp. 769-824 ◽  
Author(s):  
Keerthi Madapusi Pera
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
K3 Surfaces ◽  
Shimura Varieties ◽  
Good Reduction ◽  
Intersection Numbers ◽  
Orthogonal Groups ◽  
Canonical Models ◽  
Tate Conjecture ◽  
Precise Sense

We construct regular integral canonical models for Shimura varieties attached to Spin and orthogonal groups at (possibly ramified) primes$p>2$where the level is not divisible by$p$. We exhibit these models as schemes of ‘relative PEL type’ over integral canonical models of larger Spin Shimura varieties with good reduction at$p$. Work of Vasiu–Zink then shows that the classical Kuga–Satake construction extends over the integral models and that the integral models we construct are canonical in a very precise sense. Our results have applications to the Tate conjecture for K3 surfaces, as well as to Kudla’s program of relating intersection numbers of special cycles on orthogonal Shimura varieties to Fourier coefficients of modular forms.

A stable trace formula for Igusa varieties

2010 ◽  
Vol 9 (4) ◽  
pp. 847-895 ◽  
Author(s):  
Sug Woo Shin
Keyword(s):  
Trace Formula ◽  
Positive Characteristic ◽  
Galois Representations ◽  
Type A ◽  
Shimura Varieties ◽  
Explicit Method ◽  
Good Reduction ◽  
Orbital Integrals ◽  
Fundamental Lemma ◽  
Stable Trace Formula

AbstractIgusa varieties are smooth varieties in positive characteristic p which are closely related to Shimura varieties and Rapoport–Zink spaces. One motivation for studying Igusa varieties is to analyse the representations in the cohomology of Shimura varieties which may be ramified at p. The main purpose of this work is to stabilize the trace formula for the cohomology of Igusa varieties arising from a PEL datum of type (A) or (C). Our proof is unconditional thanks to the recent proof of the fundamental lemma by Ngô, Waldspurger and many others.An earlier work of Kottwitz, which inspired our work and proves the stable trace formula for the special fibres of PEL Shimura varieties with good reduction, provides an explicit way to stabilize terms at ∞. Stabilization away from p and ∞ is carried out by the usual Langlands–Shelstad transfer as in work of Kottwitz. The key point of our work is to develop an explicit method to handle the orbital integrals at p. Our approach has the technical advantage that we do not need to deal with twisted orbital integrals or the twisted fundamental lemma.One application of our formula, among others, is the computation of the arithmetic cohomology of some compact PEL-type Shimura varieties of type (A) with non-trivial endoscopy. This is worked out in a preprint of the author's entitled ‘Galois representations arising from some compact Shimura varieties’.

scholarly journals Potentially good reduction loci of Shimura varieties

2020 ◽  
Vol 2 (2) ◽  
pp. 399-454 ◽  
Author(s):  
Naoki Imai ◽  
Yoichi Mieda
Keyword(s):  
Shimura Varieties ◽  
Good Reduction

scholarly journals Rapoport–Zink spaces for spinor groups

2017 ◽  
Vol 153 (5) ◽  
pp. 1050-1118 ◽  
Author(s):  
Benjamin Howard ◽  
Georgios Pappas
Keyword(s):  
General Theory ◽  
Shimura Varieties ◽  
Good Theory ◽  
Good Reduction ◽  
Formal Schemes ◽  
Special Case ◽  
Canonical Integral

After the work of Kisin, there is a good theory of canonical integral models of Shimura varieties of Hodge type at primes of good reduction. The first part of this paper develops a theory of Hodge type Rapoport–Zink formal schemes, which uniformize certain formal completions of such integral models. In the second part, the general theory is applied to the special case of Shimura varieties associated with groups of spinor similitudes, and the reduced scheme underlying the Rapoport–Zink space is determined explicitly.

The Practice and Evolution of Torque and Drag Reduction: Theory and Field Results

2011 ◽  
Author(s):  
John Edward McCormick ◽  
Chad D. Evans ◽  
Joe Le ◽  
TzuFang Chiu
Keyword(s):  
Drag Reduction ◽  
Reduction Theory
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