The Action of the Morava Stabilizer Group on the Lubin-Tate Moduli Space of Lifts

1995 ◽  
Vol 117 (3) ◽  
pp. 669 ◽  
Author(s):  
Ethan S. Devinatz ◽  
Michael J. Hopkins
Keyword(s):  
Moduli Space ◽  
Morava Stabilizer Group ◽  
Stabilizer Group

scholarly journals Arithmetically defined dense subgroups of Morava stabilizer groups

2008 ◽  
Vol 144 (1) ◽  
pp. 247-270 ◽  
Author(s):  
Niko Naumann
Keyword(s):  
Abelian Variety ◽  
Modular Forms ◽  
Dense Subgroup ◽  
Maximal Orders ◽  
Topological Modular Forms ◽  
Skew Fields ◽  
Morava Stabilizer Group ◽  
Stabilizer Group ◽  
Dense Subgroups ◽  
Simple Abelian Variety

AbstractFor every prime p and integer n≥3 we explicitly construct an abelian variety $A/\mathbb {F}_{p^n}$ of dimension n such that for a suitable prime l the group of quasi-isogenies of $A/\mathbb {F}_{p^n}$ of l-power degree is canonically a dense subgroup of the nth Morava stabilizer group at p. We also give a variant of this result taking into account a polarization. This is motivated by the recent construction by Behrens and Lawson of topological automorphic forms which generalizes topological modular forms. For this, we prove some arithmetic results of independent interest: a result about approximation of local units in maximal orders of global skew fields which also gives a precise solution to the problem of extending automorphisms of the p-divisible group of a simple abelian variety over a finite field to quasi-isogenies of the abelian variety of degree divisible by as few primes as possible.

scholarly journals Picard groups of higher real -theory spectra at height

2017 ◽  
Vol 153 (9) ◽  
pp. 1820-1854 ◽  
Author(s):  
Drew Heard ◽  
Akhil Mathew ◽  
Vesna Stojanoska
Keyword(s):  
Spectral Sequence ◽  
Fixed Points ◽  
Galois Extension ◽  
Finite Subgroup ◽  
Picard Group ◽  
Picard Groups ◽  
Ring Spectra ◽  
Morava Stabilizer Group ◽  
Stabilizer Group ◽  
Homotopy Fixed Points

Using the descent spectral sequence for a Galois extension of ring spectra, we compute the Picard group of the higher real $K$-theory spectra of Hopkins and Miller at height $n=p-1$, for $p$ an odd prime. More generally, we determine the Picard groups of the homotopy fixed points spectra $E_{n}^{hG}$, where $E_{n}$ is Lubin–Tate $E$-theory at the prime $p$ and height $n=p-1$, and $G$ is any finite subgroup of the extended Morava stabilizer group. We find that these Picard groups are always cyclic, generated by the suspension.

scholarly journals The cohomology of the Morava stabilizer group ${\mathbb S}_2$ at the prime 3

1998 ◽  
Vol 126 (3) ◽  
pp. 933-941
Author(s):  
Vassily Gorbounov ◽  
Stephen F. Siegel ◽  
Peter Symonds
Keyword(s):  
Morava Stabilizer Group ◽  
Stabilizer Group

scholarly journals A DESCENT SPECTRAL SEQUENCE FOR ARBITRARY K(n)-LOCAL SPECTRA WITH EXPLICIT E2-TERM

2013 ◽  
Vol 56 (2) ◽  
pp. 369-380 ◽  
Author(s):  
DANIEL G. DAVIS ◽  
TYLER LAWSON
Keyword(s):  
Fixed Point ◽  
Positive Integer ◽  
Spectral Sequence ◽  
Cohomology Group ◽  
Adams Spectral Sequence ◽  
Continuous Cohomology ◽  
Morava Stabilizer Group ◽  
Stabilizer Group

AbstractLet n be any positive integer and p be any prime. Also, let X be any spectrum and let K(n) denote the nth Morava K-theory spectrum. Then we construct a descent spectral sequence with abutment π∗(LK(n)(X)) and E2-term equal to the continuous cohomology of Gn, the extended Morava stabilizer group, with coefficients in a certain discrete Gn-module that is built from various homotopy fixed point spectra of the Morava module of X. This spectral sequence can be contrasted with the K(n)-local En-Adams spectral sequence for π∗(LK(n)(X)), whose E2-term is not known to always be equal to a continuous cohomology group.

Topology of the quantum modified moduli space

2001 ◽  
Vol 15 (4) ◽  
pp. 279-289
Author(s):  
S. L. Dubovsky
Keyword(s):  
Moduli Space

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

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