Morava stabilizer algebras and the localization of novikov s e 2term. The iijterm of the classical adams spectral sequence hereafter abbreviated class is isomorphic to ext a z2, z2, where a is the mod 2 steenrod. Curtis the unstable adamsnovikov spectral sequence, topology 17 1978 229248. It is widely regarded as one of the main mathematics journals in the world. Periodic phenomena in the classical adams spectral sequence.
The definite article from this era is millerravenelwilson periodic phenomena in the adams novikov spectral sequence 1977. The adams novikov differentials on these classes are also. We show that the formal amodule adams novikov spectral sequence of ravenel does not naturally arise froma ltration on a map of spectra by examining the case a zi. Miller, ravenel, and wilson, periodic phenomena in the adamsnovikov spectral sequence, pdf. We investigate certain periodic phenomena in the classical adams spectral sequence which are related to the polynomial generators vn in.
The solutions to most of these conjectures by devinatz, hopkins, and. On relations between adams spectral sequences, with an application to the. Periodic phenomena in the adams novikov spectral sequence with h. The authors set up the socalled chromatic spectral sequence relating this term to the cohomology of the morava stabilizer group, which exhibits certain periodic phenomena in the adams novikov spectral sequence and can be seen as the beginning of chromatic homotopy theory. Periodic phenomena in the adamsnovikov spectral sequence jstor. The 2primary ktheory adams spectral sequence sciencedirect. Annals of mathematics is published bimonthly with the cooperation of princeton university and the institute for advanced study. Millerand ravenel, morava stabilizer algebras and the localization of novikov s e2term, 1977. Wilson in their work on the novikov spectral sequence from the point of view. Tutorial on complex multiplication of elliptic curves. These notes were taken in the homotopy theory learning.
A localization theorem in homological algebra volume 84 issue 1 haynes r. Mrw77 haynes r miller, douglas c ravenel, and w stephen wilson. Furthermore, we calculate the associated algebraic novikov spectral sequence converging to the 1line of the bp chromatic spectral sequence. E4page ofthe adams novikovspectral sequence this chart shows the adams novikov e4page through the 90stem, excluding the v1 periodic elements. Formal amodules and the adamsnovikov spectral sequence. While opinion is against the truth of the original statement, investigations of associated phenomena for a triangulated category in general have become a research. The adamsnovikov spectral sequence and the homotopy groups. The e2term of the classical adams spectral sequence hereafter abbreviated class is isomorphic to extaz2, z2, where a is the mod 2 steenrod. The classical adams spectral sequence 79 the process of investigating ext bp. We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Morava stabilizer algebras and the localization of novikov s e2term with h. Some algebraic aspects of the adamsnovikov spectral.
The purpose of this paper is to provide a similar description for the 2line of the adams novikov spectral sequence, in terms of. The nonexistence of odd primary arf invariant elements in. Then ravenel 12 formulated his conjectures on the re ection of the algebraic structure on the adams novikov e2term on the actual stable homotopy category. Realizability of the adamsnovikov spectral sequence for formal amodules tyler lawson abstract. Douglas ravenel 815 words exact match in snippet view article find links to article his most famous papers are periodic phenomena in the adams novikov spectral sequence, which he wrote together with haynes r. The lectures were given in strasbourg, may 711, 2007.
A shorter overview to the computational aspects is also contained in ravenels a novice guide to the adams novikov spectral sequence. Congruences between modular forms given by the divided family in homotopy theory mark behrens1 we characterize the 2line of the plocal adams novikov spectral sequence in terms of modular forms satisfying a certain explicit congruence condition for primes p 5. The adamsnovikov differentials on these classes are also. Some algebraic aspects of the adamsnovikov spectral sequence, thesis, princeton university, 1974. Periodic phenomena in the adams novikov spectral sequence. Miller and others published periodic phenomena in the adamsnovikov spectral sequence. In order to compare the resulting spectral sequence with the periodic homotopy groups, we model our construction on the definition in io. M1 is speriodic, and moreover s realizes the periodicity operator. Odd primary periodic phenomena in the classical adams. We investigate certain periodic phenomena in the classical adams spectral sequence which are related to the polynomial generators. These elements are analogous to the socalled arf invariant elements of order 2, hence the title. The bo adams spectral sequence mark behrens notre dame joint with agnes beaudry uchicago, prasit bhattacharya notre dame, dominic culver notre dame, zhouli xu uchicago. Adamsnovikov spectral sequence as the homotopy spectral sequence of bousfield.
Galois theory, separability, finite fields, sum of two squares, number fields and rings of integers, inertia subgroups, riemann surfaces, modular functions, elliptic functions, algebraic theory of elliptic curves. Periodic phenomena in the adams novikov spectral sequence by haynes r. Miller, on relations between adams spectral sequences, with an application to the stable homotopy of a moore space, 1981. Congruences between modular forms given by the divided. Periodic phenomena in the adams novikov spectral sequence authors. Pdf odd primary periodic phenomena in the classical. In this paper we will show that certain elements of order p p an odd prime on the 2line of the adams novikov spectral sequence support nontrivial differentials and therefore do not detect elements in the stable homotopy groups of spheres. Applying this, the authors compute the second line of the adams. The 1periodic part of the adams spectral sequence at an. At first glance see zahlers table in 75 the novikov spectral sequence appears to be less efficient than the adams spectral sequence. A spectral sequence for the homology of an in nite delooping, pac. We give a similar characterization of the 1line, reinterpreting. A chromatic resolution of the ei term of the classical adams spectral sequence is constructed. The adamsnovikov spectral sequence calculating stable homotopy groups of spheres.
Close this message to accept cookies or find out how to manage your cookie settings. Thus the 1line of the adams novikov spectral sequence is governed by the padic valuations of the denominators of the bernoulli numbers. The adamsnovikov spectral sequence and the homotopy. We study certain periodic phenomena in the cohomology of the mod p steenrod algebra which are related to the polynomial generators vn g n,bp. These are notes for a five lecture series intended to uncover largescale phenomena in the homotopy groups of spheres using the adams novikov spectral. Access denied no subscription detected were sorry, but we are unable to provide you with the full text of this article because we are not able to. Periodic phenomena in the adamsnovikov spectral sequence. The adamsnovikov spectral sequence and the homotopy groups of spheres.
Wilson, periodic phenomena in the adams novikov spectral sequence, ann. In this paper we detect invariants in the comodule consisting of. Miller, ravenel, and wilson, periodic phenomena in the adams novikov spectral sequence. We first recall the construction of the integral u, periodic. Jianguo hong, xiangjun wang submitted on 25 feb 2014 v1, last revised 26 jun 2014 this version, v2. Our names for elements are consistent with the names of elements in the cmotivic adams spectral sequence for the co. The author were partially supported by the national science foundation usa. If youve ever had a day at the end of the year when.
The adams novikov spectral sequence and the homotopy groups of spheres paul goerss. Adams spectral sequence culminated, in the late 1970s, with the work of miller, ravenel, and wilson on periodic phenomena in the homotopy groups of spheres and ravenels nilpotence conjectures. The authors would like to give their thanks to the referee for hisher many helpful suggestions on the original version of this paper, and they also acknowledge the financial support of the institute for mathematical science during their stay at the. References and resources for learning chromatic homotopy. Its e2term can be described algebraically as the cohomology of the landwebernovikov algebra of stable operations in complex cobordism. Realoriented homotopy theory and an analogue of the adams.
A nontrivial homotopy element of order p 2 detected by the. The first nontrivial differential in the former originates in. Annals of mathematics, a distinguished journal of research papers in pure mathematics, was founded in 1884. This result is also viewed as the calculation of a direct limit of localized modified adams spectral sequences converging to the homotopy of the v1 periodic. We now construct the integral u, periodic unstable novikov spectral sequence for some spaces.
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