Cycles relations in the affine grassmannian and applications to Breuil--Mézard for G-crystalline representations
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913815003660288 |
|---|---|
| author | Bartlett, Robin |
| author_facet | Bartlett, Robin |
| contents | For a split reductive group $G$ we realise identities in the Grothendieck group of $\widehat{G}$-representation in terms of cycle relations between certain closed subschemes inside the affine grassmannian. These closed subschemes are obtained as a degeneration of $e$-fold products of flag varieties and, under a bound on the Hodge type, we relate the geometry of these degenerations to that of moduli spaces of $G$-valued crystalline representations of $\operatorname{Gal}(\overline{K}/K)$ for $K/\mathbb{Q}_p$ a finite extension with ramification degree $e$. By transferring the aforementioned cycle relations to these moduli spaces we deduce one direction of the Breuil--Mézard conjecture for $G$-valued crystalline representations with small Hodge type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06455 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cycles relations in the affine grassmannian and applications to Breuil--Mézard for G-crystalline representations Bartlett, Robin Number Theory Algebraic Geometry Representation Theory For a split reductive group $G$ we realise identities in the Grothendieck group of $\widehat{G}$-representation in terms of cycle relations between certain closed subschemes inside the affine grassmannian. These closed subschemes are obtained as a degeneration of $e$-fold products of flag varieties and, under a bound on the Hodge type, we relate the geometry of these degenerations to that of moduli spaces of $G$-valued crystalline representations of $\operatorname{Gal}(\overline{K}/K)$ for $K/\mathbb{Q}_p$ a finite extension with ramification degree $e$. By transferring the aforementioned cycle relations to these moduli spaces we deduce one direction of the Breuil--Mézard conjecture for $G$-valued crystalline representations with small Hodge type. |
| title | Cycles relations in the affine grassmannian and applications to Breuil--Mézard for G-crystalline representations |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2305.06455 |