Introduction to Shimura Varieties with Bad Reduction of Parahoric Type

By Thomas J. Haines. 2004

88 citations recorded by the source corpus.

This survey article explains the construction of Rapoport-Zink local models and their use in understanding various questions relating to the singularities in the reduction modulo p of certain Shimura varieties with parahoric level structure at p.

Subfields: Mathematical Physics, Pathology and Forensic Medicine, Physiology

View Paper: https://www.semanticscholar.org/paper/561bbd2e12ad3a6480d6b23f83c7a0b50d740f5e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Georgios Pappas
2. Xuhua He
3. Michael Rapoport
4. M. Kisin
5. Xinwen Zhu
6. E. Viehmann
7. Peter Scholze
8. Thomas J. Haines

In Pathology and Forensic Medicine

1. Georgios Pappas
2. Michael Rapoport
3. M. Kisin
4. Xuhua He

In Physiology

1. Michael Rapoport
2. M. Kisin
3. Xuhua He
4. Georgios Pappas

Citations in the corpus

• Stratifications in the reduction of Shimura varieties (2015, methodology): “Non-emptiness of KR strata is due in the Siegel case to Genestier and in the fake unitary case to Haines (comp. [10, Lemma 13.1]).”
• GEOMETRIC AND HOMOLOGICAL PROPERTIES OF AFFINE DELIGNE-LUSZTIG VARIETIES (2012, methodology): “There is a close relation between the affine Deligne-Lusztig variety Xw̃(b) and the intersection of the Newton stratum associated with [b] with the Kottwitz-Rapoport stratum associated with w̃ (see [10] and [32]).”
• Integral models of Shimura varieties with parahoric level structure (2015, background): “This was first shown by Haines-Ngô for unramified unitary groups and for symplectic groups [36], and by Gaitsgory in the function field case [24].”