NYJM Logo

New York Journal of Mathematics
Volume 32 (2026), 1267-1286

  

Shane Kelly

Log homotopy types are homotopy types with modulus

view    print


Published: August 25, 2026.
Keywords: Motivic homotopy theory with modulus, logarithmic motivic homotopy theory, modulus pairs, log schemes, ramification filtrations, class field theory.
Subject [2020]: Primary 14F42; Secondary 14A21, 11R37.

Abstract
We show that the category of log homotopy types is a full subcategory of a category of homotopy types with modulus.

Acknowledgements

I thank Federico Binda and Doosung Park for answering many questions about log motives. I thank Bruno Kahn and Shuji Saito for asking questions about an earlier version of this note. I apologise to Miyazaki who, due to poor communication, wrote up a version of Theorem 1.1 independently. I also thank the many non-specialists at various conference coffee breaks who have expressed interest in this work.


Author information

Shane Kelly
Graduate School of Mathematical Sciences
University of Tokyo
3-8-1 Komaba Meguro-ku, Tokyo 153-8914, Japan

shanekelly@g.ecc.u-tokyo.ac.jp