Details
| Original language | English |
|---|---|
| Pages (from-to) | 69-116 |
| Number of pages | 48 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Volume | 2023 |
| Issue number | 796 |
| Early online date | 9 Dec 2022 |
| Publication status | Published - 1 Mar 2023 |
Abstract
We study the mod pr Milnor K-groups of p-Adically complete and p-henselian rings, establishing in particular a Nesterenko-Suslin-style description in terms of the Milnor range of syntomic cohomology. In the case of smooth schemes over complete discrete valuation rings we prove the mod pr Gersten conjecture for Milnor K-Theory locally in the Nisnevich topology. In characteristic p we show that the Bloch-Kato-Gabber theorem remains true for valuation rings, and for regular formal schemes in a pro sense.
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In: Journal fur die Reine und Angewandte Mathematik, Vol. 2023, No. 796, 01.03.2023, p. 69-116.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Milnor K-Theory of p-Adic rings
AU - Lüders, Morten
AU - Morrow, Matthew
N1 - Funding Information: The first author was supported by the DFG Research Fellowship LU 2418/1-1. The second author was partly supported by the ANR JCJC project Périodes en Géométrie Arithmétique et Motivique (ANR-18-CE40-0017). Acknowledgment: We thank Bhargav Bhatt, Dustin Clausen, and Akhil Mathew for discussions and Shuji Saito for related correspondence. We are grateful to Elden Elmanto for comments on the paper, and to the anonymous referees for various suggestions and improvements.
PY - 2023/3/1
Y1 - 2023/3/1
N2 - We study the mod pr Milnor K-groups of p-Adically complete and p-henselian rings, establishing in particular a Nesterenko-Suslin-style description in terms of the Milnor range of syntomic cohomology. In the case of smooth schemes over complete discrete valuation rings we prove the mod pr Gersten conjecture for Milnor K-Theory locally in the Nisnevich topology. In characteristic p we show that the Bloch-Kato-Gabber theorem remains true for valuation rings, and for regular formal schemes in a pro sense.
AB - We study the mod pr Milnor K-groups of p-Adically complete and p-henselian rings, establishing in particular a Nesterenko-Suslin-style description in terms of the Milnor range of syntomic cohomology. In the case of smooth schemes over complete discrete valuation rings we prove the mod pr Gersten conjecture for Milnor K-Theory locally in the Nisnevich topology. In characteristic p we show that the Bloch-Kato-Gabber theorem remains true for valuation rings, and for regular formal schemes in a pro sense.
KW - math.KT
UR - http://www.scopus.com/inward/record.url?scp=85144012998&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2101.01092
DO - 10.48550/arXiv.2101.01092
M3 - Article
AN - SCOPUS:85144012998
VL - 2023
SP - 69
EP - 116
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 796
ER -