Structure theorem for log de Rham-Witt sheaves with vanishing

TL;DR

This paper establishes a fundamental structure theorem for log de Rham-Witt sheaves with vanishing along a divisor, providing insights that support future research in Milnor K-theory with similar vanishing conditions.

Contribution

It presents a new, elegant structure theorem for log de Rham-Witt sheaves with vanishing, answering key questions posed by experts in the field.

Findings

Proves a structure theorem for log de Rham-Witt sheaves with vanishing.

Answers open questions posed by Saito and Zhao.

Lays groundwork for future study of Milnor K-theory with vanishing.

Abstract

We prove an elegant structure theorem for log de Rham-Witt sheaves with vanishing along an effective Cartier divisor $D$ defined in arXiv:2403.18763, answering a question of Shuji Saito during the Mainz conference and a question of Yigeng Zhao during a short visit of the author last summer. Our structural result for the log forms also lays the foundation for the study of Milnor $K$-theory with vanishing along $D$ in the paper to come.