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	Unramified Cohomology Of Quadrics, II (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		4 Sujatha Unramified cohomology of quadrics (context) - Kahn, Rost - 1998
		4 Sujatha Unramified cohomology of quadrics (context) - Kahn, Rost
		1 UNRAMIFIED COHOMOLOGY OF QUADRICS (context) - The, conjecture - 1996
	citeseer.ist.psu.edu /256941.html (307 words)

	[No title]
		Unramified lifting} We proceed to explain how the liftings are defined, first for unramified representations.
		Almost all the local components $\pi _{v}$ are unramified, that is contain a (unique up to a scalar multiple) nonzero $K_{v}$-fixed vector.
		The definition of lifting is extended from the case of unramified representations to that of any admissible representations.
	www.math.psu.edu /era-mirror/2004-01-005/2004-01-005.tex.html (4854 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		By an unramified map we shall mean a local homeomorphism of locally connected topological spaces that is a cosheaf space in the sense of Funk [Cahiers de Top.
		Unramified maps are a generalization of covering spaces.
		A covering space of a locally connected space is an unramified map, but over a locally path-connected and semi-locally simply connected space we establish the converse, i.e., we show that an unramified map is a covering space.
	www.pphmj.com /abstracts/jpgt/vol1issue3/ab-3.htm (209 words)

	PlanetMath: unramified action
		, the inertia subgroup, is the maximal unramified extension of
		Cross-references: extension, maximal, subgroup, fixed field, Galois theory, action, unramified, group action, inertia group, field, algebraic closures, Galois groups, residue field, maximal ideal, ring of integers, completion, prime ideal, valuation, discrete valuation, number field
		This is version 2 of unramified action, born on 2003-09-05, modified 2005-02-09.
	planetmath.org /encyclopedia/SetIsUnramifiedAtAValuation.html (136 words)

	Frobenius automorphism - Wikpedia (Site not responding. Last check: 2007-10-09)
		Given an unramified finite extension L/K of local fields, there is a concept of Frobenius automorphism which induces the Frobenius automorphism in the corresponding extension of residue fields.
		In algebraic number theory, Frobenius elements are defined for extensions L/K of global fields that are finite Galois extensions for prime ideals Φ of L that are unramified in L/K.
		Since the extension is unramified the decomposition group of Φ is the Galois group of the extension of residue fields.
	www.bostoncoop.net /~tpryor/wiki/index.php?title=Frobenius_automorphism (640 words)

	Unramified cohomology of quadrics, III, by Bruno Kahn and R. Sujatha (Site not responding. Last check: 2007-10-09)
		Unramified cohomology of quadrics, III, by Bruno Kahn and R. Sujatha
		This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4.
		We also prove that the unramified cohomology of Pfister quadrics (with divisible coefficients) always comes from the ground field, and that the same holds for their unramified Witt rings.
	www.math.uiuc.edu /K-theory/0359 (142 words)

	Creation of Local Rings and Fields
		Given a local ring or field L and a positive single precision integer n, construct the default unramified extension of L of degree n.
		If K is the residue class field of L, then the defining polynomial of the default degree n extension of K is lifted to be an inertial polynomial of L; this polynomial is used as the defining polynomial of the extension.
		Given a local ring or field L and a polynomial f with coefficients coercible to L, construct the unramified extension of L defined by f.
	modular.fas.harvard.edu /docs/magma/htmlhelp/text830.htm (1665 words)

	Unramified nonspecial real space curves having many real branches and few ovals (Site not responding. Last check: 2007-10-09)
		All unramified real curves that we constructed are nonspecial M-curves having no ovals.
		We also conjectured that any unramified real curve in even dimensional projective space is a rational normal curve.
		We showed the latter conjecture in the case of plane curves (see the paper An unramified real plane curve is a conic).
	fraise.univ-brest.fr /~huisman/rech/publications/unrscfo.html (171 words)

	Unramified Cohomology Of Quadrics, I - Kahn, Sujatha (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		Unramified Cohomology Of Quadrics, I - Kahn, Sujatha (ResearchIndex)
		Applications of these results to real quadrics and to the unramified Witt ring are given.
		Kahn, R. Sujatha, Unramified cohomology of quadrics, II, in preparation.
	citeseer.ist.psu.edu /kahn97unramified.html (887 words)

	Tables of Number Fields with Prescribed Ramification (Site not responding. Last check: 2007-10-09)
		list all fields which are unramified at all finite primes outside of S and which do ramify at every prime inside S.
		In either case, we do not separate fields based on their ramification at infinity.
		First, we have the tables for fields unramified outside of S.
	math.la.asu.edu /~jj/numberfields (400 words)

	Atlas: Signature Map and Unramified Cohomology by Jean-Philippe Monnier (Site not responding. Last check: 2007-10-09)
		Im \Lambda if and only if the graded Witt ring is isomorphic to the graded unramified cohomology ring.
		For real rational surfaces, we show that the previous condition is fulfilled and we describe completely the image of \Lambda.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-09.
	atlas-conferences.com /c/a/c/v/09.htm (183 words)

	Homework Assignment #5
		Suppose that P is unramified in every intermediate field, but ramified in L Prove that G has a unique smallest nontrivial subgroup H, and that H is normal in G; use this to show that G has prime power order, H has prime order, and H is contained in the center of G.
		Assuming further that P is unramified in L, the Frobenius automorphisms
		Prove that, if P is unramified in M, then every prime of L lying over P is unramified in LM.
	www.math.fau.edu /Klingler/alg-num-theory/hmwk5.html (884 words)

	Unramified correspondences (Site not responding. Last check: 2007-10-09)
		Then there exists an unramified cover of C which surjects onto C'.
		For any hyperelliptic curve C there is an unramified cover of degree 72 which has a surjective map of degree 4 on the curve of genus 2 given by equation y
		I will also discuss its implications (a form of effective Mordell estimates for hyperelliptic curves) and potential generalizations.
	www.math.sunysb.edu /~calendar/event.php?ID=57&Date=2002-11-21 (103 words)

	Math 254A Corrigenda
		Ramification in Galois Extensions 2: replace "b is a prime ideal which is unramified over L" with "b is a prime ideal of L which is unramified over K".
		Completions 4: "finite extension" should be "finite unramified extension".
		Since this sentence is in parentheses anyway (and I haven't defined ramified or unramified), you may ignore it if you prefer.
	www-math.mit.edu /~kedlaya/Math254A/corrigenda.html (1005 words)

	Unramified Hilbert modular forms, with examples relating to elliptic curves (Site not responding. Last check: 2007-10-09)
		Unramified Hilbert modular forms, with examples relating to elliptic curves
		Unramified Hilbert modular forms, with examples relating to elliptic curves (with Jude Socrates)
		Abstract: We give a method to explicitly determine the space of unramified Hilbert cusp forms of weight two, together with the action of Hecke, over a totally real number field of even degree and narrow class number one.
	www.cco.caltech.edu /~dw/maths/Hilbertabstract.html (165 words)

	Vignettes on automorphic and modular forms, representations, L-functions, and number theory
		Computing natural intertwining operators among unramified principal series for SL(2,R).
		The classical simplest possible example, obtaining the tensor product L-function for two holomorphic cuspforms for SL(2,Z), discussing also the Mellin-tranform trick to see the meromorphic continuation of the relevant Eisenstein series.
		Borel-Matsumoto theorem and applications to irreducibility of unramified principal series and degenerate principal series representations of reductive p-adic groups.
	www.math.umn.edu /~garrett/m/v (1093 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		A finite extension of local fields $L/K$ is called {\bf unramified} if $e(L/K)=1$.
		Then, \pen (i) $L/K$ and $L'/K$ are unramified \ff $LL'/K$ is unramified, (ii) if $L/K$ is unramified, so is $LL'/L'$ and (iii) if $L'\supseteq L$, $L'/K$ is unramified \ff $L'/L$ and $L/K$ are.
		In fact, if $L/K$ is unramified $\gal(L/K)\isom \gal(k_L/k_K)$.\sk Comments:\vsk1 We set $K^{nr}$ be the maximal unramifed extension of $K$.
	math.berkeley.edu /~coleman/Courses/Fall02/NT/35NT-02 (260 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Unramified class field theory in dimension two (Kanetomo Sato)
		Representation theory of algebraic groups over 2-dimensional local fields, using integral structures of rank 2 and translation invariant measure
		A new approach to unramified higher class field theory of arithmetic schemes
	www.maths.nottingham.ac.uk /personal/ibf/har.html (377 words)

	Centennial 2004
		Since an unramified extension has relative conductor f = 1 without any prime divisors,
		This is an application of class field theory,
		is the maximal abelian unramified 3-extension of K
	www.algebra.at /centennial2004absoluteclassfields.htm (554 words)

	Dynamical Systems in Unramified or Totally Ramified Extensions of the p-adic Number Field (Site not responding. Last check: 2007-10-09)
		Dynamical Systems in Unramified or Totally Ramified Extensions of the p-adic Number Field
		We will investigate a class of discrete dynamical systems in finite extensions of the field of p-adic numbers.
		The fixed points of the dynamical systems that we study are zeros of an irreducible polynomial of prime degree.
	www.math.ru.nl /p-adic2002/abstracts/svensson/svensson.html (63 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		\beginsection Unramified Extensions of Local Fields Suppose $(K,v)$ is a local field.
		\pr Suppose $\gp_w=(\pi)$ and $\eps \in R_L$ such that $k_L=k_K(\bar\eps)$.\vsk1 A finite extension of local fields $L/K$ is called {\bf unramified} if $e(L/K)=1$.
		Then, \pen (i) $L/K$ and $L'/K$ are unramified \ff $LL'/K$ is unramified, (ii) if $L/K$ is unramified, so is $LL'/L'$ and (iii) if $L'\supseteq L$, $L'/K$ is unramified \ff $L'/L$ and $L/K$ are.\sk \pr of (ii) Suppose $\eps\in R_L $ and $k_L=k_K(\bar\eps)$ $L=K(\eps)$ so $L'L=L'(\eps)$.
	math.berkeley.edu /~coleman/Courses/Fall02/NT/34NT-02 (241 words)

	Labesse: Noninvariant base change identities
		Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Math.
		Casselman, The unramified principal series of p-adic groups I.
		Clozel, The fundamental lemma for stable base change, Duke Math.
	www.numdam.org /numdam-bin/item?id=MSMF_1995_2_61__1_0 (442 words)

	EPrint Series of Department of Mathematics, Hokkaido University - Construction of unramified Galois extensions over ... (Site not responding. Last check: 2007-10-09)
		EPrint Series of Department of Mathematics, Hokkaido University - Construction of unramified Galois extensions over maximal abelian extensions of algebraic number fields
		Construction of unramified Galois extensions over maximal abelian extensions of algebraic number fields
		Ohtani, S (2000) Construction of unramified Galois extensions over maximal abelian extensions of algebraic number fields.
	eprints.math.sci.hokudai.ac.jp /archive/00000687 (69 words)

	DOCUMENTA MATHEMATICA, Extra Volume: Kazuya Kato's Fiftieth Birthday (2003), 789-831 (Site not responding. Last check: 2007-10-09)
		Unramified Skolem Problems and Unramified Arithmetic Bertini Theorems in Positive Characteristic
		In this paper, we prove unramified, positive-characteristic versions of theorems of Rumely and Moret-Bailly that generalized Skolem's classical problems, and unramified, positive-characteristic versions of arithmetic Bertini theorems.
		We also give several applications of these results.
	www.ii.uj.edu.pl /EMIS/journals/DMJDMV/vol-kato/tamagawa.dm.html (100 words)

	Nakagawa_Homepage
		In particular, I am interested in the distribution of the discriminants of algebraic number fields in connection with class numbers of binary forms, zeta functions associated with prehomogeneous vector spaces and Igusa's local zeta functions.
		I intend to apply the results of these research to the study of unramified Galois extensions of algebraic number fields, class numbers of algebraic number fields and Iwasawa theory.
		Class numbers of pairs of symmetric matrices, Acta Arithmetica 105, 207-225 (2002)
	www.juen.ac.jp /math/nakagawa/jin_e.html (200 words)

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