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Unstable \'etale motives
Klaus Mattis
https://arxiv.org/abs/2507.20320 https://arxiv.org/pdf/2507.20320

Unstable étale motives
We prove a rigidity result for certain $p$-complete étale $\mathbf{A}^{1}$-invariant sheaves of anima over a qcqs finite-dimensional base scheme $S$ of bounded étale cohomological dimension with $p$ invertible on $S$. This generalizes results of Suslin--Voevodsky, Ayoub, Cisinski--Déglise, and Bachmann to the unstable setting. Over a perfect field we exhibit a large class of sheaves to which our main theorem applies, in particular the $p$-completion of the étale sheafification of …

"Von der Einstellung" von Johann-Mattis List: https://wub.hypotheses.org/2895 "Ich habe […] mit mir persönlich vereinbart, dass ich mir fortan meine Forschung von niemandem mehr kaputtmachen lasse, ganz besonders nicht von mir selbst."

This https://arxiv.org/abs/2505.17081 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Lieb-Mattis ordering theorem of electronic energy levels in the thermodynamic limit
Lieb-Mattis theorem orders the lowest-energy states of total spin $s$ of a system of $P$ interacting fermions. We generalize these predictions to fermionic mixtures of $P$ particles with more than $N=2$ spinor components/species in the thermodynamic limit $P\to\infty$. The lowest-energy state inside each permutation symmetry sector $h$, arising in the $P$-fold tensor product decomposition, is well approximated by a U$(N)$ coherent (quasi-classical, variational) state, specially in the limit $P\…