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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.09392 |
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| _version_ | 1866911599582773248 |
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| author | Löwit, Jakub |
| author_facet | Löwit, Jakub |
| contents | We define a certain class of simple varieties over a field $k$ by a constructive recipe and show how to control their (equivariant) truncating invariants. Consequently, we prove that on simple varieties: (i) if $k=\overline{k}$ and $\mathrm{char} \ k = p$, the $p$-adic cyclotomic trace is an equivalence; (ii) if $k = \mathbb{Q}$, the Goodwillie-Jones trace is an isomorphism in degree zero; (iii) we can control homotopy invariant $K$-theory $KH$, which is equivariantly formal and determined by its topological counterparts. Simple varieties are quite special, but encompass important singular examples appearing in geometric representation theory. We in particular show that both finite and affine Schubert varieties for $GL_n$ lie in this class, so all the above results hold for them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant localizing invariants of simple varieties Löwit, Jakub Algebraic Geometry K-Theory and Homology We define a certain class of simple varieties over a field $k$ by a constructive recipe and show how to control their (equivariant) truncating invariants. Consequently, we prove that on simple varieties: (i) if $k=\overline{k}$ and $\mathrm{char} \ k = p$, the $p$-adic cyclotomic trace is an equivalence; (ii) if $k = \mathbb{Q}$, the Goodwillie-Jones trace is an isomorphism in degree zero; (iii) we can control homotopy invariant $K$-theory $KH$, which is equivariantly formal and determined by its topological counterparts. Simple varieties are quite special, but encompass important singular examples appearing in geometric representation theory. We in particular show that both finite and affine Schubert varieties for $GL_n$ lie in this class, so all the above results hold for them. |
| title | Equivariant localizing invariants of simple varieties |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2507.09392 |