Algebraic \(K\)-theory. Abstracts from the workshop held June 23–29, 2019.

*(English)*Zbl 1439.00065Summary: Algebraic \(K\)-theory has seen a fruitful development during the last three years. Part of this recent progress was driven by the use of \(\infty\)-categories and related techniques originally developed in algebraic topology. On the other hand we have seen continuing progress based on motivic homotopy theory which has been an important theme in relation to algebraic \(K\)-theory for twenty years.

##### MSC:

00B05 | Collections of abstracts of lectures |

00B25 | Proceedings of conferences of miscellaneous specific interest |

19-06 | Proceedings, conferences, collections, etc. pertaining to \(K\)-theory |

19Axx | Grothendieck groups and \(K_0\) |

19Exx | \(K\)-theory in geometry |

19Fxx | \(K\)-theory in number theory |

14-06 | Proceedings, conferences, collections, etc. pertaining to algebraic geometry |

14F42 | Motivic cohomology; motivic homotopy theory |

14C35 | Applications of methods of algebraic \(K\)-theory in algebraic geometry |

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\textit{T. Geisser} (ed.) et al., Oberwolfach Rep. 16, No. 2, 1737--1790 (2019; Zbl 1439.00065)

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##### References:

[1] | Fabien Morel,On the motivicπ0of the sphere spectrum, Axiomatic, enriched and motivic homotopy theory, NATO Sci. Ser. II Math. Phys. Chem., vol. 131, Kluwer Acad. Publ., Dordrecht, 2004, pp. 219-260. MR 2061856 (2005e:19002) · Zbl 1130.14019 |

[2] | Oliver R¨ondigs, Markus Spitzweck, and Paul Østvær,The first stable homotopy groups of motivic spheres, Ann. · Zbl 1406.14018 |

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