Relying on the recent work of Liu-Sz\'ekelyhidi we give a weak asymptotic estimate for Bergman kernels polarized K\"ahler manifolds with Ricci lower bound and Sobolev constant upper bound. We will also simple proof partial $C^0$ along (generalized) K\"ahler-Ricci flow Fano manifolds.

We extend the results of Deligne and Illusie on liftings modulo $p^2$ decompositions de Rham complex in several ways. show that for a smooth scheme $X$ over perfect field $k$ characteristic $p>0$, truncations $\max(p-1, 2)$ consecutive degrees can be reconstructed as objects derived category terms its truncation at most one (or, equivalently, obstruction class to lifting $p^2$). Consequently, t...

It is well known that independent (separate) encoding of $K$ correlated sources may incur some rate loss compared to joint encoding, even if the decoding done jointly. This particularly evident in multiple descriptions problem, where ...