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arXiv · 2302.10120

Non-commutative nature of $\ell$-adic vanishing cycles

Dario Beraldo·Massimo Pippi
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Abstract

Let $p:X \rightarrow S$ be a flat, proper and regular scheme over a strictly henselian discrete valuation ring. We prove that the singularity category of the special fiber with its natural two-periodic structure allows to recover the $\ell$-adic vanishing cohomology of $p$. Along the way, we compute homotopy-invariant non-connective algebraic K-theory with compact support of certain embeddings $X_t \hookrightarrow X_T$ in terms of the motivic realization of the dg category of relatively perfect complexes.

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Dario Beraldo, Massimo Pippi. 2023-02-20. Non-commutative nature of $\ell$-adic vanishing cycles. https://arxiv.org/abs/2302.10120

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