p-adic completion

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• Completion (ring theory) — In abstract algebra, a completion is any of several related functors on rings and modules that result in complete topological rings and modules. Completion is similar to localization, and together they are among the most basic tools in analysing… …   Wikipedia

• P-adic number — In mathematics, the p adic number systems were first described by Kurt Hensel in 1897 [cite journal | last = Hensel | first = Kurt | title = Über eine neue Begründung der Theorie der algebraischen Zahlen | journal =… …   Wikipedia

• p-adic number — In mathematics, and chiefly number theory, the p adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number… …   Wikipedia

• p-adic Hodge theory — In mathematics, p adic Hodge theory is a theory that provides a way to classify and study p adic Galois representations of characteristic 0 local fields[1] with residual characteristic p (such as Qp). The theory has its beginnings in Jean Pierre… …   Wikipedia

• p-adic exponential function — In mathematics, particularly p adic analysis, the p adic exponential function is a p adic analogue of the usual exponential function on the complex numbers. As in the complex case, it has an inverse function named the p adic logarithm. Contents 1 …   Wikipedia

• Commutative ring — In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Some specific kinds of commutative rings are given with …   Wikipedia

• Crystalline cohomology — In mathematics, crystalline cohomology is a Weil cohomology theory for schemes introduced by Alexander Grothendieck (1966, 1968) and developed by Pierre Berthelot (1974). Its values are modules over rings of Witt vectors over the base… …   Wikipedia

• Cauchy sequence — In mathematics, a Cauchy sequence, named after Augustin Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses. To be more precise, by dropping enough (but still only a finite number of) terms from… …   Wikipedia

• metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… …   Universalium

• Coherent duality — In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the local… …   Wikipedia

• Conductor-discriminant formula — In mathematics, the conductor discriminant formula is a formula calculating the discriminant of a finite Galois extension L / K of global fields from the global Artin conductors of the irreducible characters Irr(G) of the Galois group G = G(L /… …   Wikipedia