The motivic filtration on THH(R;Z_p) is shown to be a p-typical cyclotomic synthetic spectrum, with applications to TC and syntomic cohomology bounds.
$\mathrm{TR}$ of quasiregular semiperfect rings is even
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abstract
We show that $\mathrm{TR}_{2i+1}(S)=0$ for all $i\in \mathbb{N}$ and all $S$ quasiregular semiperfect.
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Cyclotomic synthetic spectra
The motivic filtration on THH(R;Z_p) is shown to be a p-typical cyclotomic synthetic spectrum, with applications to TC and syntomic cohomology bounds.