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International Mathematics Research Notices Advance Access originally published online on February 24, 2009
International Mathematics Research Notices (2009) 2009:2417-2475, doi:10.1093/imrn/rnp021 published on June 28, 2009
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© The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Non-adic Formal Schemes

Takehiko Yasuda

Department of Mathematics and Computer Science, Faculty of Science, Kagoshima University, 1-21-35 Korimoto, Kagoshima 890-0065, Japan

Correspondence: Correspondence to be sent to: yasuda{at}sci.kagoshi-u.ac.jp

Our purpose is to make a contribution to the foundation of the theory of formal scheme. We are interested particularly in non-Noetherian or non-adic formal schemes, which have been little studied. We redefine the formal scheme as a proringed space and study its basic properties. We also find several examples of non-adic formal schemes.

Communicated by Prof. Brian Conrad


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