Topology

Speaker: 
Jonathan Wise
Speaker Affiliation: 
University of Colorado Boulder
Speaker Link: 
https://math.colorado.edu/~jonathan.wise/

May 6, 2025

MATH 104
Canada

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Abstract: 

The logarithmic étale topology permits a logarithmic scheme to see the topology of a nearby family that has been punctured along the support of the logarithmic structure. This remarkable property allows a logarithmic scheme to see the nearby fiber of a degeneration, without requiring an explicit construction of the degeneration. It also permits the local representability of moduli problems that are not locally representable in the strict étale topology. However, the logarithmic étale topology is well known not to be subcanonical, and therefore is not suitable for descent. I will describe a coarsening of the logarithmic étale topology that remedies some of its demerits while maintaining its useful features.

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