a Witt vector is an infinite sequence of elements of a commutative ring. Ernst Witt showed how to put a ring structure on the set of Witt vectors, in...

In mathematics, the complex Witt algebra, named after Ernst Witt, is the Lie algebra of meromorphic vector fields defined on the Riemann sphere that are...

In mathematics, Witt vector cohomology was an early p-adic cohomology theory for algebraic varieties introduced by Serre (1958). Serre constructed it...

of rotations is not. Spinors are elements of a vector subspace of some Clifford algebra. Witt vector, an infinite sequence of elements of a commutative...

Shirshov–Witt theorem Witt algebra Witt decomposition Witt design (Witt geometry) Witt group Witt index Witt polynomial Witt ring Grothendieck-Witt ring Witt scheme...

worked together on Witt vectors. In two papers around 2014, they simplified the theory by giving a presentation of the ring of Witt vectors in terms of a completion...

1991, shortly after his 80th birthday. Witt's work has been highly influential. His invention of the Witt vectors clarifies and generalizes the structure...

mathematics, a Witt ring may be A ring of Witt vectors The Witt ring (forms), a ring structure on the Witt group of symmetric bilinear forms See also Witt algebra...

S2CID 119143902. Bhatt, Bhargav; Scholze, Peter (2017). "Projectivity of the Witt vector affine Grassmannian". Inventiones Mathematicae. 209 (2): 329–423. arXiv:1507...

characteristic p of p-power degree (not just degree p itself), using Witt vectors, developed by Witt (1936). Artin, Emil; Schreier, Otto (1927), "Eine Kennzeichnung...

In vector calculus, a complex lamellar vector field is a vector field which is orthogonal to a family of surfaces. In the broader context of differential...

non-commutative Dieudonné ring, which is generated over the ring of Witt vectors by two special endomorphisms F {\displaystyle F} and V {\displaystyle...

in the construction of Morava E-theory in chromatic homotopy theory. Witt vector Artin–Hasse exponential Group functor Addition theorem Note that the...

is given in the article on Witt vectors, where they provide an important role in providing a ring structure. Witt vector Section 4.3 of Cohen, Henri...

symmetric bilinear form with a norm 0 vector. Each class is represented by the core form of a Witt decomposition. The Witt group of k is the abelian group W(k)...

field Group scheme of roots of unity Dirichlet character Ramanujan's sum Witt vector Teichmüller character Hadlock, Charles R. (2000). Field Theory and Its...

Amongst Serre's early candidate theories of 1954–55 was one based on Witt vector coefficients. Around 1958 Serre suggested that isotrivial principal bundles...

coefficients in Witt vectors of k. F and V are the Frobenius and Verschiebung operators, and they may act nontrivially on the Witt vectors. Dieudonne and...

p-adic integers. Examples (in roughly historical order) include: Serre's Witt vector cohomology Monsky–Washnitzer cohomology Infinitesimal cohomology Crystalline...

over a base field k. Its values Hn(X/W) are modules over the ring W of Witt vectors over k. It was introduced by Alexander Grothendieck (1966, 1968) and...

more specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the...

define the Witt group W(k) which describes the "stable" theory of quadratic forms over the field k. Let (V, b) be a finite-dimensional vector space over...

above). Another important property of perfect fields is that they admit Witt vectors. More generally, a ring of characteristic p (p a prime) is called perfect...

the Poincaré–Birkhoff–Witt theorem. Gröbner bases are also sometimes called standard bases. In physics, the standard basis vectors for a given Euclidean...

Hahn series can be combined with Witt vectors (at least over a perfect field) to form twisted Hahn series or Hahn–Witt series: for example, over a finite...

\textstyle \prod _{n\geq 0}(1{-}t^{n})^{-a_{n}}} . Witt vector Hazewinkel, Michiel (2009). "Witt vectors I". Handbook of Algebra. Vol. 6. Elsevier/North-Holland...

the Frobenius homomorphism. It was introduced by Witt (1937) as the shift operator on Witt vectors taking (a0, a1, a2, ...) to (0, a0, a1, ...). ("Verschiebung"...

{\displaystyle \delta (x)={\frac {\sigma (x)-x^{p}}{p}}} defines a p-derivation. Witt vector Arithmetic derivative Derivation Fermat quotient Buium, Alex (1989),...

transcendental over F p ( x ) {\displaystyle \mathbb {F} _{p}(x)} . Witt vector Formal group Artin, E.; Hasse, H. (1928), "Die beiden Ergänzungssätze...

the finite field of order p. Taking A to be a ring of truncated Witt vectors gives Witt's generalization of Artin–Schreier theory to extensions of exponent...