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57
Elliptic spectra, the Witten genus and the theorem of the cube
 Invent. Math
, 1997
"... 2. More detailed results 7 2.1. The algebraic geometry of even periodic ring spectra 7 ..."
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Cited by 63 (16 self)
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2. More detailed results 7 2.1. The algebraic geometry of even periodic ring spectra 7
The sigma orientation is an H∞ map
 American Journal of Mathematics
"... Abstract. In [AHS01] the authors constructed a natural map, called the sigma orientation, from the Thom spectrum MU〈6 〉 to any elliptic spectrum in the sense of [Hop95]. MU〈6 〉 is an H ∞ ring spectrum, and in this paper we show that if (E, C, t) is the elliptic spectrum associated to the universal d ..."
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Cited by 15 (2 self)
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Abstract. In [AHS01] the authors constructed a natural map, called the sigma orientation, from the Thom spectrum MU〈6 〉 to any elliptic spectrum in the sense of [Hop95]. MU〈6 〉 is an H ∞ ring spectrum, and in this paper we show that if (E, C, t) is the elliptic spectrum associated to the universal deformation of a supersingular elliptic curve over a perfect field of characteristic p> 0, then the sigma orientation is a map of H ∞ ring spectra.
Morita theory for Hopf algebroids and presheaves of groupoids
 Amer. J. Math
"... Abstract. Comodules over Hopf algebroids are of central importance in algebraic topology. It is wellknown that a Hopf algebroid is the same thing as a presheaf of groupoids on Aff, the opposite category of commutative rings. We show in this paper that a comodule is the same thing as a quasicoheren ..."
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Cited by 14 (2 self)
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Abstract. Comodules over Hopf algebroids are of central importance in algebraic topology. It is wellknown that a Hopf algebroid is the same thing as a presheaf of groupoids on Aff, the opposite category of commutative rings. We show in this paper that a comodule is the same thing as a quasicoherent sheaf over this presheaf of groupoids. We prove the general theorem that internal equivalences of presheaves of groupoids with respect to a Grothendieck topology T on Aff give rise to equivalences of categories of sheaves in that topology. We then show using faithfully flat descent that an internal equivalence in the flat topology gives rise to an equivalence of categories of quasicoherent sheaves. The corresponding statement for Hopf algebroids is that weakly equivalent Hopf algebroids have equivalent categories of comodules. We apply this to formal group laws, where we get considerable generalizations of the MillerRavenel [MR77] and HoveySadofsky [HS99] change of rings theorems in algebraic topology.
Appendix to Twisted Loop Groups and their affine flag varieties by
 Advances in Math. 219
, 2008
"... Loop groups are familiar objects in several branches of mathematics. Let us mention here three variants. The first variant is differentialgeometric in nature. One starts with a Lie group G (e.g., a compact Lie group or its complexification). The associated loop group is then the group ..."
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Cited by 13 (3 self)
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Loop groups are familiar objects in several branches of mathematics. Let us mention here three variants. The first variant is differentialgeometric in nature. One starts with a Lie group G (e.g., a compact Lie group or its complexification). The associated loop group is then the group
(Pre)sheaves of Ring Spectra over the Moduli Stack of Formal Group Laws
, 2004
"... In the first part of this article, I will state a realization problem for diagrams of structured ring spectra, and in the second, I will discuss the moduli space which parametrizes the problem. ..."
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Cited by 12 (1 self)
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In the first part of this article, I will state a realization problem for diagrams of structured ring spectra, and in the second, I will discuss the moduli space which parametrizes the problem.
The essential dimension of the normalizer of a maximal torus in the projective linear group. Algebra Number Theory
"... Abstract. Let p be a prime, k be a field of characteristic = p containing a primitive pth root of unity and N be the normalizer of the maximal torus in the projective linear group PGLn. We compute the exact value of the essential dimension edk(N; p) of N at p for every n≥1. Contents ..."
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Cited by 12 (6 self)
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Abstract. Let p be a prime, k be a field of characteristic = p containing a primitive pth root of unity and N be the normalizer of the maximal torus in the projective linear group PGLn. We compute the exact value of the essential dimension edk(N; p) of N at p for every n≥1. Contents
Formal schemes and formal groups
 in honor of J.M. Boardman, volume 239 of Contemporary Mathematics
, 1999
"... 1.1. Notation and conventions 3 1.2. Even periodic ring spectra 3 2. Schemes 3 ..."
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Cited by 8 (6 self)
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1.1. Notation and conventions 3 1.2. Even periodic ring spectra 3 2. Schemes 3
Existence of quotients by finite groups and coarse moduli spaces
 Aug 2007, arXiv:0708.3333v1. D. RYDH
"... Abstract. In this paper we prove the existence of several quotients in a very general setting. We consider finite group actions and more generally groupoid actions with finite stabilizers generalizing the results of Keel and Mori. In particular we show that any algebraic stack with finite inertia st ..."
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Cited by 8 (3 self)
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Abstract. In this paper we prove the existence of several quotients in a very general setting. We consider finite group actions and more generally groupoid actions with finite stabilizers generalizing the results of Keel and Mori. In particular we show that any algebraic stack with finite inertia stack has a coarse moduli space. We also show that any algebraic stack with quasifinite diagonal has a locally quasifinite flat cover. The proofs do not use noetherian methods and are valid for general algebraic spaces and algebraic stacks.