M. Ohara

activity

20142021

collaborators

6 papers

math.AT2021

The 23-rd and 24-th homotopy groups of the n-th rotation group

Yoshihiro Hirato, Jin-ho Lee, Toshiyuki Miyauchi +2

We denote by $π_{k} (R_{n})$ the $k$ -th homotopy group of the $n$ -th rotation group $R_{n}$ and $π_{k} (R_{n} : 2)$ the 2-primary components of it. We determine the group structures of $π_k(R_n:…

math.KT2020

Cotorsion pairs in Hopfological algebra

Mariko Ohara, Dai Tamaki

In an intriguing paper arXiv:math/0509083 Khovanov proposed a generalization of homological algebra, called Hopfological algebra. Since then, several attempts have been made to imp…

math.KT2018

On graded $E_{\infty}$ -rings and projective schemes in spectral algebraic geometry

Mariko Ohara, Takeshi Torii

We introduce graded $E_{\infty}$ -rings and graded modules over them, and study their properties. We construct projective schemes associated to connective $N$ -grad…

math.AT2017

On Mimura's extension problem

Toshiyuki Miyauchi, Juno Mukai, Mariko Ohara

We determine the group strucure of the $23$ -rd homotopy group $π_{23} (G_{2} : 2)$ , where $G_{2}$ is the Lie group of exceptional type, which hasn't been determined for $50$ years.

math.KT2016

Algebraic K-theory of finitely projective modules on $E_{\infty}$ -rings

Mariko Ohara

In this paper, we study the K-theory on higher modules in spectral algebraic geometry. We relate the K-theory of an $\infty$ -category of finitely generated projective modules on ce…

math.KT2014

A representation for algebraic K-theory of quasi-coherent modules over affine spectral schemes