Cyclotomic boundedness I
Hot Topics: Life after the Telescope Conjecture December 09, 2024 - December 13, 2024
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Hesselholt–Madsen proved the Lichtenbaum–Quillen conjecture for p-adic local fields K (with p > 2) by proving the stronger statement that V (1)∗TR(OK) is bounded. Bounded TR is now best interpreted as boundedness in the Antieau–
Nikolaus t-structure. The speaker will introduce this t-structure, and note that THH(Fp) is bounded. The main aim of the talk should be to characterize cyclotomic boundedness in more concrete terms, as the combination of the Segal conjecture and canonical vanishing. Bounded cyclotomic rings admit a B ̈okstedt class, and the speaker will discuss its basic properties.
Suggested references: Sections 2.2, 2.3 and 2.4 of [AN21]
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