Continuous Valuations and the Adic Spectrum
نویسندگان
چکیده
Following [Hub93, §3], we introduce the spectrum of continuous valuations Cont(A) for a Huber ring A and the adic spectrum Spa(A,A) for a Huber pair (A,A). We also draw heavily from [Con14; Wed12]. These notes are from the arithmetic geometry learning seminar on adic spaces held at the University of Michigan during the Winter 2017 semester, organized by Bhargav Bhatt. See [Dat17; Ste17] for other notes from the seminar.
منابع مشابه
Arithmetic Geometry Learning Seminar: Adic Spaces
1. January 12th – Motivation (Bhargav Bhatt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2. January 26th – Huber rings (Rankeya Datta). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملp-adic Shearlets
The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.
متن کاملOn 3-adic Valuations of Generalized Harmonic Numbers
We investigate 3-adic valuations of generalized harmonic numbers H n . These valuations are completely determined by the 3-adic expansion of n. Moreover, we also give 3-adic valuations of generalized alternating harmonic numbers.
متن کامل$p$-adic Dual Shearlet Frames
We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...
متن کاملVALUATIONS OF p-ADIC REGULATORS OF CYCLIC CUBIC FIELDS
We compute the p-adic regulator of cyclic cubic extensions of Q with discriminant up to 1016 for 3 < p < 100, and observe the distribution of the p-adic valuation of the regulators. We find that for almost all primes the observation matches the model that the entries in the regulator matrix are random elements with respect to the obvious restrictions. Based on this random matrix model a conject...
متن کامل