Peter Scholze and Jared Weinstein
- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691202082
- eISBN:
- 9780691202150
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691202082.003.0003
- Subject:
- Mathematics, Geometry / Topology
This chapter defines adic spaces. A scheme is a ringed space which locally looks like the spectrum of a ring. An adic space will be something similar. The chapter then identifies the adic version of ...
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This chapter defines adic spaces. A scheme is a ringed space which locally looks like the spectrum of a ring. An adic space will be something similar. The chapter then identifies the adic version of “locally ringed space.” Briefly, it is a topologically ringed topological space equipped with valuations. The chapter also reflects on the role of A+ in the definition of adic spaces. The subring A+ in a Huber pair may seem unnecessary at first: why not just consider all continuous valuations on A? Specifying A+ keeps track of which inequalities have been enforced among the continuous valuations. Finally, the chapter differentiates between sheafy and non-sheafy Huber pairs.Less
This chapter defines adic spaces. A scheme is a ringed space which locally looks like the spectrum of a ring. An adic space will be something similar. The chapter then identifies the adic version of “locally ringed space.” Briefly, it is a topologically ringed topological space equipped with valuations. The chapter also reflects on the role of A+ in the definition of adic spaces. The subring A+ in a Huber pair may seem unnecessary at first: why not just consider all continuous valuations on A? Specifying A+ keeps track of which inequalities have been enforced among the continuous valuations. Finally, the chapter differentiates between sheafy and non-sheafy Huber pairs.
