Algebraic K-theory of quasi-smooth blow-ups and cdh descent

We construct a semi-orthogonal decomposition on the category of perfect complexes on the blow-up of a derived Artin stack in a quasi-smooth centre. This gives a generalization of Thomason's blow-up formula in algebraic K-theory to derived stacks. We also provide a new criterion for descent in Voevodsky's cdh topology, which we use to give a direct proof of Cisinski's theorem that Weibel's homotopy invariant K-theory satisfies cdh descent.Comment: 24 pages; to appear in Annales Henri Lebesgu

Lorentz violation and Condensed Matter Physics

We present heuristic arguments that hint to a possible connection of Lorentz violation with observed phenomenon in condensed matter physics. Various references from condensed matter literature are cited where operators in the Standard Model Extension appear to be enhanced. Furthermore, we consider the Levy-Leblond equation, which is the analogue of Dirac equation in non-relativistic quantum mechanics. We show that we can obtain the Levy-Leblond equation by adding enhanced Lorentz violating operators to the Dirac equation. Based on these observations, we propose that Lorentz violation exhibits itself in non-relativistic quantum mechanics.Comment: 11 pages, 1 Tabl