Borcherds products approximating Gersten complex
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918296720244736 |
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| author | Ma, Shouhei |
| author_facet | Ma, Shouhei |
| contents | For an orthogonal modular variety, we construct a complex which is defined in terms of lattices and elliptic modular forms, which resembles the Gersten complex in Milnor K-theory, and which has a morphism to the Gersten complex of the modular variety by the Borcherds lifting. This provides a formalism for approaching the higher Chow groups of the modular variety by special cycles and Borcherds products. The construction is an incorporation of the theory of Borcherds products and ideas from Milnor K-theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13643 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Borcherds products approximating Gersten complex Ma, Shouhei Algebraic Geometry K-Theory and Homology Number Theory 11F55, 19D45, 14C15 For an orthogonal modular variety, we construct a complex which is defined in terms of lattices and elliptic modular forms, which resembles the Gersten complex in Milnor K-theory, and which has a morphism to the Gersten complex of the modular variety by the Borcherds lifting. This provides a formalism for approaching the higher Chow groups of the modular variety by special cycles and Borcherds products. The construction is an incorporation of the theory of Borcherds products and ideas from Milnor K-theory. |
| title | Borcherds products approximating Gersten complex |
| topic | Algebraic Geometry K-Theory and Homology Number Theory 11F55, 19D45, 14C15 |
| url | https://arxiv.org/abs/2601.13643 |