Lectures on Logarithmic Algebraic Geometry

  title={Lectures on Logarithmic Algebraic Geometry},
  author={Arthur Ogus},
  • A. Ogus
  • Published 31 October 2018
  • Mathematics

Intrinsic Mirror Symmetry

We associate a ring R to a log Calabi-Yau pair (X,D) or a degeneration of Calabi-Yau manifolds X->B. The vector space underlying R is determined by the tropicalization of (X,D) or X->B, while the

A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology

. This paper incorporates the theory of Hochschild homology into our program on log motives. We discuss a geometric definition of logarithmic Hochschild homology of derived pre-log rings and construct

Motives and homotopy theory in logarithmic geometry

This document is a short user’s guide to the theory of motives and homotopy theory in the setting of logarithmic geometry. We review some of the basic ideas and results in relation to other works on

Formality of little disks and algebraic geometry

We construct a canonical chain of formality quasiisomorphisms for the operad of chains on framed little disks and the operad of chains on little disks. The construction is done in terms of

Logarithmic differentials on discretely ringed adic spaces

On a smooth discretely ringed adic space $\mathcal{X}$ over a field $k$ we define a subsheaf $\Omega_{\mathcal{X}}^+$ of the sheaf of differentials $\Omega_{\mathcal{X}}$. It is defined in a similar

Logarithmic differentials on discretely ringed adic spaces

On a smooth discretely ringed adic space X over a field k we define a subsheaf Ω+X of the sheaf of differentials ΩX . It is defined in a similar way as the subsheaf O X of OX using Kähler seminorms

Les suites spectrales de Hodge-Tate

This book presents two important results in p-adic Hodge theory following the approach initiated by Faltings, namely (i) his main p-adic comparison theorem, and (ii) the Hodge-Tate spectral sequence.

Moduli of framed formal curves

We introduce framed formal curves, which are formal algebraic curves with boundary components parametrized by the punctured formal disk. We study the moduli space of nodal framed formal curves, which

On relative and overconvergent de Rham–Witt cohomology for log schemes

We construct the relative log de Rham–Witt complex. This is a generalization of the relative de Rham–Witt complex of Langer–Zink to log schemes. We prove the comparison theorem between the

Analytic semi-universal deformations in logarithmic complex geometry

  • Raffaele Caputo
  • Mathematics
    Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
  • 2023
We show that every compact complex analytic space endowed with a fine logarithmic structure and every morphism between such spaces admit a semi-universal deformation. These results generalize the



Algebraic geometry

  • R. Hartshorne
  • Mathematics, Computer Science
    Graduate texts in mathematics
  • 1977
It’s better to think of Algebraic Geometry as indicating a sub-area of mathematics as a whole, rather than a very precisely defined subfield.

An overview of the work of K. Fujiwara, K. Kato, and C. Nakayama on logarithmic étale cohomology

Ce texte presente les travaux de K. Fujiwara, K. Kato et C. Nakayama sur la cohomologie log etale des log schemas. Apres quelques rappels sur le langage des log schemas, nous definissons et etudions