number theory, a compatible system of ℓ-adic representations is an abstraction of certain important families of ℓ-adic Galois representations, indexed by prime...

and the Galois representations on ℓ-adic cohomology groups of algebraic varieties. Unlike Artin representations, ℓ-adic representations can have infinite...

the χℓ form a strictly compatible system of ℓ-adic representations. The p-adic cyclotomic character is the p-adic Tate module of the multiplicative group...

the p-adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; p-adic numbers...

as numbers by number theorists. The p-adic numbers play an important role in this analogy. Some number systems that are not included in the complex numbers...

_{p}} of p-adic numbers as well as over the ring Z p {\displaystyle \mathbb {Z} _{p}} of p-adic integers. Part of Claude Chevalley's construction of the...

2-adic addition and multiplication compatible with two's complement representation. Continuity of binary arithmetical and bitwise operations in 2-adic metric...

theory p-adic analysis a branch of number theory that deals with the analysis of functions of p-adic numbers. p-adic dynamics an application of p-adic analysis...

an alternate metric completion of ⁠ Q {\displaystyle \mathbb {Q} } ⁠, one can define a p-adic Lie group over the p-adic numbers, a topological group which...

mathematics, particularly number theory, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were...

viewing the set of infinite strings as the inverse limit of the sets of finite strings. This is the construction used for the p-adic numbers and some...

absolute value or a p-adic absolute value. Dyadic rational Floating point Ford circles Gaussian rational Naive height—height of a rational number in lowest...

in terms of generators and relations is also known for the Galois groups of p-adic number fields (finite extensions of Qp). Representations of Galois groups...

duality. The bounded derived category of perverse l-adic sheaves on a scheme X is equivalent to the derived category of constructible sheaves and similarly...

either the set of integers modulo p (i.e., the set of congruence classes of integers), or the set of p-adic integers. The whole numbers were synonymous with...

thought", International Forum of Psychoanalysis, 17 (4): 201-212. Murtagh, F. (2012), "Ultrametric Model of Mind, I: Review", P-Adic Numbers, Ultrametric Analysis...

zeros of a p-adic L-function with the eigenvalues of an operator, so can be thought of as an analogue of the Hilbert–Pólya conjecture for p-adic L-functions...

formed from any other topological field, such as the field of complex numbers or the field of p-adic numbers. These examples are locally compact, so they have...

starting from 1, while columns representing the independent variables use 26-adic bijective numeration using the letters A-Z as numerals. Its physical size...

cohomology of a ring R and, in high enough degrees and after completing at a prime l invertible in R, abut to the l-adic completion of the K-theory of R. In...

Lusztig, George (1983), "Some examples of square integrable representations of semisimple p-adic groups", Trans. Amer. Math. Soc., 277: 623–653, doi:10...