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Rost nilpotence for twisted Milnor hypersurfaces
Charles De Clercq, Evan Marth, Kirill Zainoulline
https://arxiv.org/abs/2510.07095 https://arxiv.org/pdf/2…

Rost nilpotence for twisted Milnor hypersurfaces
We show that the strong Rost nilpotence holds for motives of generic hyperplane sections of twisted Milnor hypersurfaces. Hence, we provide a new family of examples of smooth projective algebraic varieties which satisfy the strong Rost nilpotence principle. As an application, we compute the $p$-canonical dimension for such varieties.

The spectral Sullivan conjecture
Ishan Levy
https://arxiv.org/abs/2510.00262 https://arxiv.org/pdf/2510.00262

The spectral Sullivan conjecture
We show that any map from an infinite loop space to a $p$-complete nilpotent finite dimensional space factors canonically through a union of $p$-adic tori. This is proven via bootstrapping from the case of $B\mathbb{Z}/p\mathbb{Z}$, which is the key case of the Sullivan conjecture proven by Miller. The main step in our proof is to show that the subcategory of spectra generated by the reduced suspension spectrum of $B\mathbb{Z}/p\mathbb{Z}$ under colimits and extensions agrees with that of a Moo…