p-adic iterated integration on semistable curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913886112841728 |
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| author | Katz, Eric Litt, Daniel |
| author_facet | Katz, Eric Litt, Daniel |
| contents | We reformulate the theory of p-adic iterated integrals on semistable curves using the unipotent log rigid fundamental group. This fundamental group carries Frobenius and monodromy operators whose basic properties are established. By identifying the Frobenius-invariant subgroup of the fundamental group with the fundamental group of the dual graph, we characterize Berkovich--Coleman integration, which is path-dependent, as integration along the Frobenius-invariant lift of a path in the dual graph. Vologodsky's path-independent integration theory which was previously described using a monodromy condition can now be identified as Berkovich--Coleman integration along a combinatorial canonical path arising from the theory of combinatorial iterated integration as developed by the first-named author and Cheng. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_05340 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | p-adic iterated integration on semistable curves Katz, Eric Litt, Daniel Algebraic Geometry Number Theory We reformulate the theory of p-adic iterated integrals on semistable curves using the unipotent log rigid fundamental group. This fundamental group carries Frobenius and monodromy operators whose basic properties are established. By identifying the Frobenius-invariant subgroup of the fundamental group with the fundamental group of the dual graph, we characterize Berkovich--Coleman integration, which is path-dependent, as integration along the Frobenius-invariant lift of a path in the dual graph. Vologodsky's path-independent integration theory which was previously described using a monodromy condition can now be identified as Berkovich--Coleman integration along a combinatorial canonical path arising from the theory of combinatorial iterated integration as developed by the first-named author and Cheng. |
| title | p-adic iterated integration on semistable curves |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2202.05340 |