Results 1  10
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102
Topological Tits alternative
 the Annals of Math
, 2004
"... Abstract. Let k be a local field, and Γ ≤ GLn(k) a linear group over k. We prove that either Γ contains a relatively open solvable subgroup, or it contains a relatively dense free subgroup. This result has applications in dynamics, Riemannian foliations and profinite groups. 1. ..."
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Abstract. Let k be a local field, and Γ ≤ GLn(k) a linear group over k. We prove that either Γ contains a relatively open solvable subgroup, or it contains a relatively dense free subgroup. This result has applications in dynamics, Riemannian foliations and profinite groups. 1.
Homotopy fixed points for LK(n)(En ∧X) using the continuous action
 J. Pure Appl. Algebra
"... Abstract. Let K(n) be the nth Morava Ktheory spectrum. Let En be the LubinTate spectrum, which plays a central role in understanding LK(n)(S 0), the K(n)local sphere. For any spectrum X, dene E_(X) to be the spectrum LK(n)(En ^ X). Let G be a closed subgroup of the pronite group Gn, the group of ..."
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Cited by 20 (14 self)
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Abstract. Let K(n) be the nth Morava Ktheory spectrum. Let En be the LubinTate spectrum, which plays a central role in understanding LK(n)(S 0), the K(n)local sphere. For any spectrum X, dene E_(X) to be the spectrum LK(n)(En ^ X). Let G be a closed subgroup of the pronite group Gn, the group of ring spectrum automorphisms of En in the stable homotopy category. We show that E_(X) is a continuous Gspectrum, with homotopy xed point spectrum (E_(X))hG. Also, we construct a descent spectral sequence with abutment ((E_(X))hG): 1.
The universal covering homomorphism in ominimal expansions of groups
 Math. Logic Quart
, 2007
"... Suppose that G is a definably connected, definable group in an ominimal expansion of an ordered group. We show that the ominimal universal covering homomorphism p ̃ : G ̃ − → G is a locally definable covering homomorphism and pi1(G) is isomorphic to the ominimal fundamental group pi(G) of G defin ..."
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Cited by 16 (6 self)
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Suppose that G is a definably connected, definable group in an ominimal expansion of an ordered group. We show that the ominimal universal covering homomorphism p ̃ : G ̃ − → G is a locally definable covering homomorphism and pi1(G) is isomorphic to the ominimal fundamental group pi(G) of G defined using locally definable covering homomorphisms.
PERMANENCE CRITERIA FOR SEMIFREE PROFINITE GROUPS
, 810
"... Dedicated to Moshe Jarden on the occasion of his 65th birthday ..."
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Cited by 13 (3 self)
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Dedicated to Moshe Jarden on the occasion of his 65th birthday
Iterated homotopy fixed points for the LubinTate spectrum
, 2006
"... When G is a profinite group and H and K are closed subgroups, with H normal in K, it is not always possible to form the iterated homotopy fixed point spectrum (ZhH) hK/H, where Z is a continuous Gspectrum. However, we show that, if G = Gn, the extended Morava stabilizer group, and Z = ̂ L(En ∧ X ..."
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Cited by 12 (9 self)
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When G is a profinite group and H and K are closed subgroups, with H normal in K, it is not always possible to form the iterated homotopy fixed point spectrum (ZhH) hK/H, where Z is a continuous Gspectrum. However, we show that, if G = Gn, the extended Morava stabilizer group, and Z = ̂ L(En ∧ X), where ̂ L is Bousfield localization with respect to Morava Ktheory, En is the LubinTate spectrum, and X is any spectrum with trivial Gnaction, then the iterated homotopy fixed point spectrum can always be constructed. Also, we show that (EhH n of Devinatz and Hopkins.) hK/H is just E hK
Homotopy fixed points for L K(n)(En∧ X) using the continuous action
 J. Pure Appl. Algebra
"... Abstract. Let G be a closed subgroup of Gn, the extended Morava stabilizer group. Let En be the LubinTate spectrum, X an arbitrary spectrum with trivial Gaction, and let ˆ L = L K(n). We prove that ˆ L(En ∧ X) is a continuous Gspectrum with homotopy fixed point spectrum ( ˆ L(En ∧ X)) hG, define ..."
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Cited by 12 (5 self)
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Abstract. Let G be a closed subgroup of Gn, the extended Morava stabilizer group. Let En be the LubinTate spectrum, X an arbitrary spectrum with trivial Gaction, and let ˆ L = L K(n). We prove that ˆ L(En ∧ X) is a continuous Gspectrum with homotopy fixed point spectrum ( ˆ L(En ∧ X)) hG, defined with respect to the continuous action. Also, we construct a descent spectral sequence whose abutment is π∗( ( ˆ L(En∧X)) hG). We show that the homotopy fixed points of ˆ L(En ∧ X) come from the K(n)localization of the homotopy fixed points of the spectrum (Fn ∧ X). 1.
Classification of the simple factors appearing in composition series of totally disconnected contraction groups
, 2006
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SPECTRAL PROPERTIES OF LIMITPERIODIC SCHRÖDINGER OPERATORS
, 2009
"... We investigate the spectral properties of Schrödinger operators in ℓ²(Z) with limitperiodic potentials. The perspective we take was recently proposed by Avila and is based on regarding such potentials as generated by continuous sampling along the orbits of a minimal translation of a Cantor group. ..."
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Cited by 12 (7 self)
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We investigate the spectral properties of Schrödinger operators in ℓ²(Z) with limitperiodic potentials. The perspective we take was recently proposed by Avila and is based on regarding such potentials as generated by continuous sampling along the orbits of a minimal translation of a Cantor group. This point of view allows one to separate the base dynamics and the sampling function. We show that for any such base dynamics, the spectrum is a Cantor set of positive Lebesgue measure and purely absolutely continuous for a dense set of sampling functions, and it is a Cantor set of zero Lebesgue measure and purely singular continuous for a dense Gδ set of sampling functions.
Additive Structure of Multiplicative Subgroups of Fields and Galois Theory
 DOCUMENTA MATH.
, 2004
"... One of the fundamental questions in current field theory, related to Grothendieck’s conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classificati ..."
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Cited by 11 (5 self)
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One of the fundamental questions in current field theory, related to Grothendieck’s conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classification of additive properties of multiplicative subgroups of fields containing all squares, using pro2Galois groups of nilpotency class at most 2, and of exponent at most 4. This work extends some powerful methods and techniques from formally real fields to general fields of characteristic not 2.
The LubinTate spectrum and its homotopy fixed point spectra
 NORTHWESTERN UNIVERSITY
, 2003
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