Project description

Logarithmic structures on ordinary rings were introduced in algebraic geometry by Kato, Fontaine and Illusie. In recent years, this concept has been successfully generalized to the structured ring spectra of stable homotopy theory. One aim of this project is to develop a notion of differential graded algebras with logarithmic structures and to define interesting examples for these. The resulting "logarithmic dgas" will provide new examples for ring spectra with logarithmic structures. Moreover, they may help to understand arithmetic properties of dgas and shed new light on the passage from dgas to ring spectra.

Related publications

Published Articles

Birgit Richter, Brooke Shipley, An algebraic model for commutative H$\mathbb{Z}$-algebras, Algebr. Geom. Topol. 17 (2017), no. 4, 2013--2038.

Irina Bobkova, Ayelet Lindenstrauss, Kate Poirier, Birgit Richter, Inna Zakharevich, On the higher topological Hochschild homology of $\mathbb{F}_p$ and commutative $\mathbb{F}_p$-group algebras, in: Women in Topology: Collaborations in Homotopy Theory. Contemporary Mathematics 641, AMS, 2015, 97--122.

Birgit Richter, On the homology and homotopy of commutative shuffle algebras, Israel Journal of Mathematics 209 (2), 2015, 651--682.

John Rognes, Steffen Sagave, and Christian Schlichtkrull, Localization sequences for logarithmic topological Hochschild homology, Mathematische Annalen, 363 (2015), no. 3, 1349–1398

Birgit Richter, Steffen Sagave. A strictly commutative model for the cochain algebra of a space. Compos. Math. 156 (2020), no. 8, 1718--1743.

Gemma Halliwell, Eva Höning, Ayelet Lindenstrauss, Birgit Richter, Inna Zakharevich, Relative Loday constructions and applications to higher THH-calculations, Topology and its Applications 235 (2018), 523--545.

Bjørn Ian Dundas, Ayelet Lindenstrauss, Birgit Richter, On higher topological Hochschild homology of rings of integers, Math. Research Letters 25, 2 (2018), 489--507.

John Rognes, Steffen Sagave, and Christian Schlichtkrull, Logarithmic topological Hochschild homology of topological K-theory spectra, J. Eur. Math. Soc. (JEMS) 20 (2018), no. 2, 489--527.

Bjørn Ian Dundas, Ayelet Lindenstrauss, Birgit Richter, Towards an understanding of ramified extensions of structured ring spectra, Mathematical Proceedings of the Cambridge Philosophical Society 168 (3) (2020), 435--454.

Birgit Richter, Commutative ring spectra arXiv:1710.02328 to appear in: Stable categories and structured ring spectra, edited by Andrew J. Blumberg, Teena Gerhardt, and Michael A. Hill, MSRI Book Series, Cambridge University Press.

Preprints