ترغب بنشر مسار تعليمي؟ اضغط هنا

The Brown-Peterson spectrum is not $E_{2(p^2+2)}$ at odd primes

68   0   0.0 ( 0 )
 نشر من قبل Andrew Senger
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Andrew Senger




اسأل ChatGPT حول البحث

Recently, Lawson has shown that the 2-primary Brown-Peterson spectrum does not admit the structure of an $E_{12}$ ring spectrum, thus answering a question of May in the negative. We extend Lawsons result to odd primes by proving that the p-primary Brown-Peterson spectrum does not admit the structure of an $E_{2(p^2+2)}$ ring spectrum. We also show that there can be no map $MU to BP$ of $E_{2p+3}$ ring spectra at any prime.

قيم البحث

اقرأ أيضاً

85 - Tyler Lawson 2017
The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the Brown-Peterson spectrum. We will construct a secondary operation in mod-2 homology and show that this canonical subalgebra is not closed under it. This allows us t o conclude that the 2-primary Brown-Peterson spectrum does not admit the structure of an E_n-algebra for any n greater than or equal to 12, answering a question of May in the negative.
We calculate the homotopy type of $L_1L_{K(2)}S^0$ and $L_{K(1)}L_{K(2)}S^0$ at the prime 2, where $L_{K(n)}$ is localization with respect to Morava $K$-theory and $L_1$ localization with respect to $2$-local $K$ theory. In $L_1L_{K(2)}S^0$ we find a ll the summands predicted by the Chromatic Splitting Conjecture, but we find some extra summands as well. An essential ingredient in our approach is the analysis of the continuous group cohomology $H^ast_c(mathbb{G}_2,E_0)$ where $mathbb{G}_2$ is the Morava stabilizer group and $E_0 = mathbb{W}[[u_1]]$ is the ring of functions on the height $2$ Lubin-Tate space. We show that the inclusion of the constants $mathbb{W} to E_0$ induces an isomorphism on group cohomology, a radical simplification.
We calculate the homotopy type of the Brown-Comenetz dual $I_2$ of the K(2)-local sphere at the prime 3 and show that there is a twisting by a non-trivial element $P$ in the exotic part of the Picard group. We give a complete characterization of $P$ as well. The main technique is to give a sequence of calculations of the homotopy groups of elements of the Picard group after smashing with the Smith-Toda complex V(1).
Fix the base field Q of rational numbers and let BP<n> denote the family of motivic truncated Brown-Peterson spectra over Q. We employ a local-to-global philosophy in order to compute the motivic Adams spectral sequence converging to the bi-graded ho motopy groups of BP<n>. Along the way, we provide a new computation of the homotopy groups of BP<n> over the 2-adic rationals, prove a motivic Hasse principle for the spectra BP<n>, and deduce several classical and recent theorems about the K-theory of particular fields.
The $ER(2)$-cohomology of $Bmathbb{Z}/(2^q)$ and $mathbb{C}P^n$ are computed along with the Atiyah-Hirzebruch spectral sequence for $ER(2)^*(mathbb{C}P^infty)$. This, along with other papers in this series, gives us the $ER(2)$-cohomology of all Eile nberg-MacLane spaces. Since $ER(2)$ is $TMF_0(3)$ after a suitable completion, these computations also take care of that theory.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا