The formal degree conjecture for groups over local function fields
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913161794289664 |
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| author | B, Anantha Krishna |
| author_facet | B, Anantha Krishna |
| contents | In this article, we will prove that the formal degree conjecture is compatible with the Deligne-Kazhdan correspondence for quasi-split groups, assuming that the local Langlands correspondence is compatible with the Deligne-Kazhdan correspondence. Consequently, we establish the formal degree conjecture for $\operatorname{GL}_n$ over local function fields of characteristic $p > 0$, and for $\operatorname{Sp}_{2n}$, split $\operatorname{SO}_{2n}$, $\operatorname{SO}_{2n+1}$, and $\operatorname{GSp}_4$ over local function fields of characteristic $p > 2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_26031 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The formal degree conjecture for groups over local function fields B, Anantha Krishna Representation Theory 22E50, 11F70 In this article, we will prove that the formal degree conjecture is compatible with the Deligne-Kazhdan correspondence for quasi-split groups, assuming that the local Langlands correspondence is compatible with the Deligne-Kazhdan correspondence. Consequently, we establish the formal degree conjecture for $\operatorname{GL}_n$ over local function fields of characteristic $p > 0$, and for $\operatorname{Sp}_{2n}$, split $\operatorname{SO}_{2n}$, $\operatorname{SO}_{2n+1}$, and $\operatorname{GSp}_4$ over local function fields of characteristic $p > 2$. |
| title | The formal degree conjecture for groups over local function fields |
| topic | Representation Theory 22E50, 11F70 |
| url | https://arxiv.org/abs/2605.26031 |