A note on lattices in semi-stable representations

By Tongyin Liu. 2007

88 citations recorded by the source corpus.

Let p be a prime, K a finite extension over $${{\mathbb Q}_p}$$ and $${G = {\rm Gal}(\overline K /K)}$$ . We extend Kisin’s theory on $${\varphi}$$ -modules of finite E(u)-height to give a new classification of G-stable $${{\mathbb Z}1_p}$$ -lattices in semi-stable representations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0779281473f65225bc8dbd7a87205b3170c4ad82

How researchers see this paper

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

In Geometry and Topology

1. T. Gee
2. Peter Scholze
3. David Savitt
4. B. Bhatt
5. Tongyin Liu
6. Kiran S. Kedlaya
7. M. Kisin
8. M. Emerton

In Mathematical Physics

1. T. Gee
2. Peter Scholze
3. David Savitt
4. B. Bhatt
5. Tongyin Liu
6. M. Kisin
7. Kiran S. Kedlaya
8. M. Emerton

Citations in the corpus

• Prismatic $F$-crystals and crystalline Galois representations (2021, methodology): “…DSπ (L) ⊗Sπ Ainf and Dπ′(L) ⊗Sπ′ Ainf are identified in a (ϕ,GK)-equivariant manner; here the implicit GK-action on the base change is not automatic from [Kis06], and in fact is the main result of [Liu10] (but it is already uniquely determined by the given GK -action on the étale realization).”
• The buzzard-diamond-jarvis conjecture for unitary groups (2012, methodology): “One can show that RK0 and R̂ are stable under the action of GK and that the GK-action factors through Ĝ (see [Liu10b, §2.2]).”