On Deformation Theory in Higher Logarithmic Geometry
Year: 2025
Type: article
Abstract: We initiate the study of deformation theory in the context of derived and higher log geometry. After reconceptualizing the ‘exactification’-procedures in ordinary log geometry in terms of Quillen’s approach to the cotangent complex, we construct an “tangent bundle’ over the category of log ring spectra. The fibers recover the categories of modules over the underlying ring spectra, and the resulting cotangent complex functor specializes to log topological André–Quillen homology on each fiber. As applications, we characterize log square-zero extensions and derive a log variant of étale rigidity, applicable to some tamely ramified extensions of ring spectra.
Author: Tommy Lundemo
Institution: University of Wuppertal
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4407714775