Lectures on Logarithmic Algebraic Geometry

A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.

Arthur Ogus (Author)

9781107187733, Cambridge University Press

Hardback, published 8 November 2018

558 pages
23.5 x 15.8 x 3.5 cm, 0.9 kg

'The book under review is a self-contained exposition of the foundations of logarithmic geometry and would serve as a standard textbook for graduate students on this subject. The approach is scheme-theoretic, therefore the reader only needs to have a basic knowledge of algebraic geometry.' Yigeng Zhao, zbMATH

This graduate textbook offers a self-contained introduction to the concepts and techniques of logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry and number theory. It features a systematic exposition of the foundations of the field, from the basic results on convex geometry and commutative monoids to the theory of logarithmic schemes and their de Rham and Betti cohomology. The book will be of use to graduate students and researchers working in algebraic, analytic, and arithmetic geometry as well as related fields.

1. The geometry of monoids
2. Sheaves of monoids
3. Logarithmic schemes
4. Differentials and smoothness
5. Betti and de Rham cohomology.

Subject Areas: Algebraic geometry [PBMW]