Logarithmic geometry and algebraic stacks

Martin C. Olsson

Displaying similar documents to “Logarithmic geometry and algebraic stacks”

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

Takeshi Tsuji (2000)

Bulletin de la Société Mathématique de France

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$F$ -crystals on schemes with constant log structure

Arthur Ogus (1995)

Compositio Mathematica

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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.

Endomorphisms of logarithmic schemes

Mark Kisin (2003)

Rendiconti del Seminario Matematico della Università di Padova

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Mixed Hodge structures on log deformations

Taro Fujisawa, Chikara Nakayama (2003)

Rendiconti del Seminario Matematico della Università di Padova

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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.

Ramification of local fields with imperfect residue fields. II.

Abbes, Ahmed, Saito, Takeshi (2003)

Documenta Mathematica

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Tame stacks in positive characteristic

Dan Abramovich, Martin Olsson, Angelo Vistoli (2008)

Annales de l’institut Fourier

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We introduce and study a class of algebraic stacks with finite inertia in positive and mixed characteristic, which we call tame algebraic stacks. They include tame Deligne-Mumford stacks, and are arguably better behaved than general Deligne-Mumford stacks. We also give a complete characterization of finite flat linearly reductive schemes over an arbitrary base. Our main result is that tame algebraic stacks are étale locally quotient by actions of linearly reductive finite group schemes. ...