Endomorphisms of logarithmic schemes

Mark Kisin

Displaying similar documents to “Endomorphisms of logarithmic schemes”

On the $p$ adic nearby cycles of log smooth families

Takeshi Tsuji (2000)

Bulletin de la Société Mathématique de France

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On the conductor formula of Bloch

Kazuya Kato, Takeshi Saito (2004)

Publications Mathématiques de l'IHÉS

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In [6], S. Bloch conjectures a formula for the Artin conductor of the ℓ-adic etale cohomology of a regular model of a variety over a local field and proves it for a curve. The formula, which we call the conductor formula of Bloch, enables us to compute the conductor that measures the wild ramification by using the sheaf of differential 1-forms. In this paper, we prove the formula in arbitrary dimension under the assumption that the reduced closed fiber has normal crossings.

Prime to $p$ fundamental groups and tame Galois actions

Mark Kisin (2000)

Annales de l'institut Fourier

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We show that for a local, discretely valued field $F$ , with residue characteristic $p$ , and a variety $𝒰$ over $F$ , the map $ρ : Gal (F^{sep} / F) \to Out (π_{1, geom}^{(p^{'})} (𝒰))$ to the outer automorphisms of the prime to $p$ geometric étale fundamental group of $𝒰$ maps the wild inertia onto a finite image. We show that under favourable conditions $ρ$ depends only on the reduction of $𝒰$ modulo a power of the maximal ideal of $F$ . The proofs make use of the theory of logarithmic schemes.