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Longer titles found: Discrete valuation ring (view)

searching for Valuation ring 15 found (95 total)

Levi-Civita field (1,213 words) [view diff] exact match in snippet view article find links to article

corresponding to the first non zero coefficient of a Levi-Civita series. The valuation ring is that of series bounded by real numbers, the residue field is R {\displaystyle

P-adically closed field (1,142 words) [view diff] exact match in snippet view article find links to article

of v {\displaystyle v} (the residue field being the quotient of the valuation ring { x ∈ F : w ( x ) ≥ 0 } {\displaystyle \{x\in F:w(x)\geq 0\}} by its

Warfield group (61 words) [view diff] exact match in snippet view article find links to article

"Classification theorems for p-groups and modules over a discrete valuation ring" (PDF), Bulletin of the American Mathematical Society, 78: 88–92, doi:10

Artin approximation theorem (497 words) [view diff] exact match in snippet view article find links to article

Artin (1969). Let R {\displaystyle R} be a field or an excellent discrete valuation ring, let A {\displaystyle A} be the henselization at a prime ideal of an

Chevalley's structure theorem (521 words) [view diff] exact match in snippet view article find links to article

connected component of the closed fiber of a Neron model over a discrete valuation ring is an algebraic group, which is in general neither affine nor proper

Flat topology (1,100 words) [view diff] exact match in snippet view article find links to article

we can consider the local ring Rx at this point, which is a discrete valuation ring whose spectrum has one closed point and one open (generic) point. We

Dimension of a scheme (1,254 words) [view diff] exact match in snippet view article find links to article

dim ⁡ U = dim ⁡ X {\displaystyle \dim U=\dim X} . Let R be a discrete valuation ring and X = A R 1 = Spec ⁡ ( R [ t ] ) {\displaystyle X=\mathbb {A} _{R}^{1}=\operatorname

Degeneration (algebraic geometry) (596 words) [view diff] exact match in snippet view article

says Let X be a normal irreducible projective scheme over a discrete valuation ring. If the generic fiber is ruled, then each irreducible component of the

Takeshi Saito (mathematician) (307 words) [view diff] case mismatch in snippet view article

Takeshi (1987). "Vanishing Cycles and Geometry of Curves Over a Discrete Valuation Ring". American Journal of Mathematics. 109 (6): 1043–1085. doi:10.2307/2374585

Irving Kaplansky (2,095 words) [view diff] exact match in snippet view article find links to article

MR 0059895. Kaplansky, Irving (1953). "Dual modules over a valuation ring. I". Proc. Amer. Math. Soc. 4 (2): 213–219. doi:10.1090/s0002-9939-1953-0053092-7

Gopal Prasad (1,799 words) [view diff] exact match in snippet view article find links to article

Yu determined all the quasi-reductive group schemes over a discrete valuation ring (DVR), [25]. In collaboration with Brian Conrad and Ofer Gabber, Prasad

Ramification group (2,557 words) [view diff] exact match in snippet view article find links to article

equivalence class [w] ∈ Sv. Let mw denote the maximal ideal of w inside the valuation ring Rw of w. The inertia group of w is the subgroup Iw of Gw consisting

Localized Chern class (766 words) [view diff] exact match in snippet view article find links to article

pure-dimensional regular scheme of finite type over a field or discrete valuation ring and X a closed subscheme. Let E ∙ {\displaystyle E_{\bullet }} denote

H topology (1,860 words) [view diff] exact match in snippet view article find links to article

Spec(R/{\mathfrak {p}})\sqcup Spec(R_{\mathfrak {p}})\to Spec(R)} where R is a valuation ring of rank 2 and p {\displaystyle {\mathfrak {p}}} is the non-open, non-closed

Surreal number (11,406 words) [view diff] exact match in snippet view article find links to article

of the leading term in the Conway normal form, e.g., ν(ω) = −1. The valuation ring then consists of the finite surreal numbers (numbers with a real and/or