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Motives with modulus over a base

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KAH2 - K-theory, algebraic cycles and motivic homotopy theory

Kahn, Miyazaki, Saito, Yamazaki’s theory of motives (over a field) with modulus formalises the idea of ramification filtration / irregular singularities in a Voevodsky-esque framework. After giving some motivation for this theory, I’ll describe how to extend it to a general qcqs base with modulus. In particular, mixed characteristic and non-noetherian valuation rings are allowed. Along the way, we obtain a natural definition of homotopy type with modulus, and various Grothendieck topologies closely related to the relative Riemann-Zariski spaces of Temkin.

This talk is part of the Isaac Newton Institute Seminar Series series.

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