Ramification theory from homotopical point of view, I

Abstract

We prove the compatibility of pushforward along a proper morphism of an étale constructible sheaf and the pushforward of its characteristic cycle up to $p$-torsion. This was conjectured by Takeshi Saito. For this, we revisit the construction of the characteristic cycle, due to Saito and Beilinson, from more homotopical point of view. In particular, the language of $\infty$-categories is indispensable to carry this out.

Some proofs were simplified based on the referee's feedback. See the Introduction for further details on these changes

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