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Witt vector affine Springer fibers

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arxiv 2404.09945 v2 pith:HF232FE3 submitted 2024-04-15 math.AG math.NT

Witt vector affine Springer fibers

Jingren Chi This is my paper
classification math.AG math.NT
keywords affinefibersspringercharacteristicgroupvectorwittartin
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We establish dimension formulas for the Witt vector affine Springer fibers associated to a reductive group over a mixed characteristic local field, under the assumption that the group is essentially tamely ramified and the residue characteristic is not bad. Besides the discriminant valuations that show up in classical works on the usual affine Springer fibers, our formula also involves the Artin conductors and the Kottwitz invariants of the relevant conjugacy classes.

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  1. Equivalued affine springer fibers in mixed characteristic

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    Proves that tame equi-valued Witt-vector affine Springer fibers admit pavings by perfections of iterated affine space bundles over smooth Hessenberg varieties and establishes a Chevalley restriction theorem for dual L...