p-adic

Etymology
From. The letter follows common number theory usage in representing an arbitrary prime number; the suffix  signals that properties of the number p (generally, those due to its being prime, and specifically those of a specified p) are fundamental to the theory and determine the properties of the resulting construction.

Adjective

 * 1)  Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers.
 * 2) * 1997, Fernando Q. Gouvêa, p-adic Numbers: An Introduction, Springer, 2nd Edition, page 60,
 * Definition 3.3.3 The ring of p-adic integers is the valuation ring
 * $$\Z_p = \{x \in \Q_p : |x|_p \le 1\}$$.
 * 1) * 2007, Nguyen Minh Cheung, Nguyen Van Co, Le Quang Thuan, §12: Harmonic Analysis Over P-adic Field I: Some Equations and Singular Field Operators, N. M. Chuong, Yu V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford (editors), Harmonic, Wavelet and P-adic Analysis, World Scientific, page 272,
 * The paper is organized as follows:
 * 2. Preliminaries
 * 3. A p-adic Cauchy problem
 * 4. The p-adic Hilbert transform
 * 5. The boundaries in the p-adic space $$L^q$$
 * 5. The boundaries in the p-adic space $$L^q$$

Usage notes
The synonym is used in some contexts: for instance, in regard to Galois representations (G-modules, where the Galois group G is  a vector space over the field of ℓ-adic numbers), and in algebraic geometry, where ℓ-adic cohomology is one of the "classical" constructions of.

Synonyms

 * ℓ-adic

Translations

 * Catalan: p-àdic
 * Finnish: p-adinen
 * French: p-adique
 * German: p-adisch
 * Italian: p-adico
 * Polish: p-adyczny
 * Portuguese: p-ádico
 * Romanian: p-adic
 * Spanish: p-ádico