Periodic phenomena in the adams novikov spectral sequence pdf

We investigate certain periodic phenomena in the classical adams spectral sequence which are related to the polynomial generators. The adams novikov differentials on these classes are also. A novices guide to the adamsnovikov spectral sequence. Adamsnovikov spectral sequence as the homotopy spectral sequence of bousfield. Pdf odd primary periodic phenomena in the classical. Furthermore, we calculate the associated algebraic novikov spectral sequence converging to the 1line of the bp chromatic spectral sequence. The definite article from this era is millerravenelwilson periodic phenomena in the adams novikov spectral sequence 1977. The purpose of this paper is to provide a similar description for the 2line of the adams novikov spectral sequence, in terms of. 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. Periodic phenomena in the adamsnovikov spectral sequence. We first recall the construction of the integral u, periodic. These notes were taken in the homotopy theory learning.

Close this message to accept cookies or find out how to manage your cookie settings. E4page ofthe adams novikovspectral sequence this chart shows the adams novikov e4page through the 90stem, excluding the v1 periodic elements. 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. While opinion is against the truth of the original statement, investigations of associated phenomena for a triangulated category in general have become a research.

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Some algebraic aspects of the adamsnovikov spectral sequence, thesis, princeton university, 1974. We give a similar characterization of the 1line, reinterpreting. The lectures were given in strasbourg, may 711, 2007. 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. Wilson in their work on the novikov spectral sequence from the point of view. Periodic phenomena in the adamsnovikov spectral sequence jstor. Morava stabilizer algebras and the localization of novikov s e 2term.

The adamsnovikov spectral sequence and the homotopy groups of spheres. 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. Furthermore, we calculate the associated algebraic novikov spectral. These elements are analogous to the socalled arf invariant elements of order 2, hence the title. 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. Annals of mathematics is published bimonthly with the cooperation of princeton university and the institute for advanced study. Periodic phenomena in the classical adams spectral sequence. The solutions to most of these conjectures by devinatz, hopkins, and. Odd primary periodic phenomena in the classical adams. The 1periodic part of the adams spectral sequence at an. In this paper we detect invariants in the comodule consisting of.

Tutorial on complex multiplication of elliptic curves. 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. 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. The 2primary ktheory adams spectral sequence sciencedirect. Our names for elements are consistent with the names of elements in the cmotivic adams spectral sequence for the co. If youve ever had a day at the end of the year when. Formal amodules and the adamsnovikov spectral sequence. Applying this, the authors compute the second line of the adams. In order to compare the resulting spectral sequence with the periodic homotopy groups, we model our construction on the definition in io. Miller, on relations between adams spectral sequences, with an application to the stable homotopy of a moore space, 1981. A chromatic resolution of the ei term of the classical adams spectral sequence is constructed. The nonexistence of odd primary arf invariant elements in. Annals of mathematics, a distinguished journal of research papers in pure mathematics, was founded in 1884. A shorter overview to the computational aspects is also contained in ravenels a novice guide to the adams novikov spectral sequence.

At first glance see zahlers table in 75 the novikov spectral sequence appears to be less efficient than the adams spectral sequence. Miller, ravenel, and wilson, periodic phenomena in the adamsnovikov spectral sequence, pdf. Some algebraic aspects of the adamsnovikov spectral. Thus the 1line of the adams novikov spectral sequence is governed by the padic valuations of the denominators of the bernoulli numbers. We now construct the integral u, periodic unstable novikov spectral sequence for some spaces. Periodic phenomena in the adams novikov spectral sequence with h. The e2term of the classical adams spectral sequence hereafter abbreviated class is isomorphic to extaz2, z2, where a is the mod 2 steenrod. We investigate certain periodic phenomena in the classical adams spectral sequence which are related to the polynomial generators vn in. The adamsnovikov differentials on these classes are also. The adamsnovikov spectral sequence and the homotopy. Miller and others published periodic phenomena in the adamsnovikov spectral sequence.

A localization theorem in homological algebra volume 84 issue 1 haynes r. Realizability of the adamsnovikov spectral sequence for formal amodules tyler lawson abstract. Stephen wilson introduction the problem of understanding the stable homotopy ring has long been one of the touchstones of algebraic topology. Morava stabilizer algebras and the localization of novikov s e2term with h. Realoriented homotopy theory and an analogue of the adams. 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. Periodic phenomena in the adams novikov spectral sequence.

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. Congruences between modular forms given by the divided. The author were partially supported by the national science foundation usa. 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. A nontrivial homotopy element of order p 2 detected by the.

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. It is widely regarded as one of the main mathematics journals in the world. The first nontrivial differential in the former originates in. Periodic phenomena in the adams novikov spectral sequence by haynes r. 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. Wilson, periodic phenomena in the adams novikov spectral sequence, ann. These are notes for a five lecture series intended to uncover largescale phenomena in the homotopy groups of spheres using the adams novikov spectral. Periodic phenomena in the adams novikov spectral sequence authors.

Millerand ravenel, morava stabilizer algebras and the localization of novikov s e2term, 1977. 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. 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. Mrw77 haynes r miller, douglas c ravenel, and w stephen wilson. Miller, ravenel, and wilson, periodic phenomena in the adams novikov spectral sequence. Curtis the unstable adamsnovikov spectral sequence, topology 17 1978 229248. Jianguo hong, xiangjun wang submitted on 25 feb 2014 v1, last revised 26 jun 2014 this version, v2. M1 is speriodic, and moreover s realizes the periodicity operator. The adamsnovikov spectral sequence and the homotopy groups. The adams novikov spectral sequence and the homotopy groups of spheres paul goerss. On relations between adams spectral sequences, with an application to the.