On the uniform positivity of $F$-signature under reduction modulo $p$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912496790536192 |
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| author | Takagi, Shunsuke Yamaguchi, Tatsuki |
| author_facet | Takagi, Shunsuke Yamaguchi, Tatsuki |
| contents | Carvajal-Rojas, Schwede and Tucker asked whether the mod $p$ reductions of a complex klt type singularity have uniformly positive $F$-signature for almost all primes $p$. In this paper, we give an affirmative answer to this conjecture in the case of pure subrings of regular local rings--for example, reductive quotient singularities. We also show that the conjecture can be reduced to the Gorenstein case. Finally, we discuss the connection with $F$-alpha invariants--a characteristic $p$ analog of Tian's alpha invariants introduced by Pande--for log Fano pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the uniform positivity of $F$-signature under reduction modulo $p$ Takagi, Shunsuke Yamaguchi, Tatsuki Algebraic Geometry Commutative Algebra 13A35, 14B05, 14J17 Carvajal-Rojas, Schwede and Tucker asked whether the mod $p$ reductions of a complex klt type singularity have uniformly positive $F$-signature for almost all primes $p$. In this paper, we give an affirmative answer to this conjecture in the case of pure subrings of regular local rings--for example, reductive quotient singularities. We also show that the conjecture can be reduced to the Gorenstein case. Finally, we discuss the connection with $F$-alpha invariants--a characteristic $p$ analog of Tian's alpha invariants introduced by Pande--for log Fano pairs. |
| title | On the uniform positivity of $F$-signature under reduction modulo $p$ |
| topic | Algebraic Geometry Commutative Algebra 13A35, 14B05, 14J17 |
| url | https://arxiv.org/abs/2507.16566 |