Related papers: Redshift and multiplication for truncated Brown-Pe…

We prove the $K(n)$-local analogue of the Hahn-Wilson conjecture on fp-spectra, which states that the truncated Brown-Peterson spectra generate the category of fp-spectra as a thick subcategory. As a corollary, we deduce the original…

For a perfectoid ring $R$ and a natural number $n$ we investigate the essential image of the category of truncated by $n$ Barsotti-Tate groups under the anti-equivalence between commutative, finite, locally free, $R$-group schemes of…

For any n-by-n complex matrix T and any $1\leqslant k\leqslant n$, let $\Lambda_{k}(T)$ the set of all $\lambda\in \C$ such that $PTP=\lambda P$ for some rank-k orthogonal projection $P$ be its higher rank-k numerical range. It is shown…

Our results are of three types. First we describe a general procedure of adjoining polynomial variables to $A_\infty$-ring spectra whose coefficient rings satisfy certain restrictions.A host of examples of such spectra is provided by…

We develop a more general view of Stembridge's enriched $P$-partitions and use this theory to outline the structure of peak algebras for the symmetric group and the hyperoctahedral group. Initially we focus on commutative peak algebras,…

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…

We study the algebraic $K$-theory of rings of the form $R[x]/x^e$. We do this via trace methods and filtrations on topological Hochschild homology and related theories by quasisyntomic sheaves. We produce computations for $R$ a perfectoid…

We describe an iterable construction of THH for an E_n ring spectrum. The reduced version is an iterable bar construction and its n-th iterate gives a model for the shifted cotangent complex at the augmentation, representing reduced…

We construct commutative algebra spectra that represent the operator $K$-theory of $C^*$-algebras, which are algebras over the commutative ring spectra that represent topological $K$-theory. The spectral multiplicative structure introduces…

We construct an algorithm for solving the following problem: given a number field $K$, a positive integer $N$, and a positive real number $B$, determine all points in $\mathbb P^N(K)$ having relative height at most $B$. A theoretical…

The spectrum of baryons containing three b quarks is calculated in nonperturbative QCD, using the lattice regularization. The energies of ten excited bbb states with J^P = 1/2^+, 3/2^+, 5/2^+, 7/2^+, 1/2^-, and 3/2^- are determined with…

Let $k$ be a number field and $S$ a finite set of places of $k$ containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of $S$-integers of $k$. Moreover, we give an…

Since long-lived light bottom squark (sbottom) and its anti-particle with a mass close to the bottom quark have not been excluded by experiments so far, we consider such a sbottom to combine with its anti-particle to form a color singlet…

We generalize Stembridge's enriched $P$-partitions and use this theory to outline the structure of peak algebras for the symmetric group and the hyperoctahedral group. Whereas Stembridge's enriched $P$-partitions are related to…

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…

Let $p$ be an odd prime and let $\mathit{EO} = E_{p-1}^{hC_p}$ be the $C_p$ fixed points of height $p-1$ Morava $E$ theory. We say that a spectrum $X$ has algebraic $\mathit{EO}$ theory if the splitting of $K_*(X)$ as an $K_*[C_p]$-module…

We prove a higher chromatic analogue of Snaith's theorem which identifies the K-theory spectrum as the localisation of the suspension spectrum of CP^\infty away from the Bott class; in this result, higher Eilenberg-MacLane spaces play the…

The formation of a deeply-bound $K^- pp$ state with $I=1/2$, $J^\pi=0^-$ by the $^3$He(in-flight $K^-$, $n$) reaction is theoretically investigated in a distorted-wave impulse approximation using the Green's function method. The expected…

Let $G$ be a finite group, $\Omega(G)$ be its Burnside ring, and $\Delta(G)$ its augmentation ideal. Denote by $\Delta^n(G)$ and $Q_n(G)$ the $n$-th power of $\Delta(G)$ and the $n$-th consecutive quotient group…

We obtain lower bounds on the rank of the kappa ring of the Delign-Mumford compactification of the moduli space of curves in different degrees. For this purpose, we introduce a quotient of the kappa ring, the combinatorial kappa ring, and…