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SUMMARY:Syntomic cohomology of regular ring spectra - Gabriel Angelini-kno
 ll (Université Paris 13)
DTSTART:20250617T104500Z
DTEND:20250617T114500Z
UID:TALK230707@talks.cam.ac.uk
DESCRIPTION:Work of Hahn and Wilson demonstrated that many qualitative que
 stions about algebraic K-theory and the arithmetic of ring spectra can be 
 answered using a suitable filtration of topological cyclic homology\, whic
 h closely approximates algebraic K-theory. Hahn\, Raksit\, and Wilson late
 r observed that this filtration fits into a general paradigm\, which also 
 recovers filtrations previously studied by Bhatt&mdash\;Morrow&mdash\;Scho
 lze\, Antieau\, Morin\, and Bhatt&mdash\;Lurie. I will report on&nbsp\; so
 me applications of this technology to ring spectra such as real topologica
 l K-theory\,&nbsp\; Morava K-theory\, truncated Brown&mdash\;Peterson spec
 tra\, and topological modular forms. In particular\, these explicit comput
 ations give examples where the Mahowald&mdash\;Rezk telescope conjecture h
 olds and the Ausoni&mdash\;Rognes&mdash\;Lichtenbaum&mdash\;Quillen conjec
 ture holds. Each of these projects are joint with some subset of my co-aut
 hors Ausoni\, Bruner\, Davies\, Hahn\, Rognes\, Wilson\, and Yang.
LOCATION:Seminar Room 1\, Newton Institute
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