On admissible tensor products in pp-adic Hodge theory

We prove that if $W$ and $W'$ are two $B$-pairs whose tensor product is crystalline (or semi-stable or de Rham or Hodge-Tate), then there exists a character $\mu$ such that $W(\mu^{-1})$ and $W'(\mu)$ are crystalline (or semi-stable or de Rham or Hodge-Tate). We also prove that if $W$ is a $B$-pair and $F$ is a Schur functor (for example \Sym^n(-) or $\Lambda^n(-)$) such that $F(W)$ is crystalline (or semi-stable or de Rham or Hodge-Tate) and if the rank of $W$ is sufficiently large, then there is a character $\mu$ such that $W(\mu^{-1})$ is crystalline (or semi-stable or de Rham or Hodge-Tate). In particular, these results apply to $p$-adic representations

Might Carbon-Atmosphere White Dwarfs Harbour a New Type of Pulsating Star?

In the light of the recent and unexpected discovery of a brand new type of white dwarfs, those with carbon-dominated atmospheres, we examine the asteroseismological potential of such stars. The motivation behind this is based on the observation that past models of carbon-atmosphere white dwarfs have partially ionized outer layers that bear strong resemblance with those responsible for mode excitation in models of pulsating DB (helium-atmosphere) and pulsating DA (hydrogen-atmosphere) white dwarfs. Our exciting main result is that, given the right location in parameter space, some carbon-atmosphere white dwarfs are predicted to show pulsational instability against gravity modes. We are eagerly waiting the results of observational searches for luminosity variations in these stars.Comment: 4-page letter + 4 figure

Motivation and Performance, Blog 7

Student blog posts from the Great VCU Bike Race Book

Filtered modules corresponding to potentially semi-stable representations

We classify the filtered modules with coefficients corresponding to two-dimensional potentially semi-stable $p$-adic representations of the absolute Galois groups of $p$-adic fields under the assumptions that $p$ is odd and the coefficients are large enough.Comment: 19 page

Paraboline variation of pp-adic families of (φ,Γ)(\varphi,\Gamma)-modules

We study the $p$-adic variation of triangulations over $p$-adic families of $(\varphi,\Gamma)$-modules. In particular, we study certain canonical sub-filtrations of the pointwise triangulations and show that they extend to affinoid neighborhoods of crystalline points. This generalizes results of Kedlaya, Pottharst and Xiao and (independently) Liu in the case where one expects the entire triangulation to extend. As an application, we study the ramification of weight parameters over natural $p$-adic families.Comment: 46 pages (larger font than before). Final version. Numerous improvements to expositions and corrections of minor errors. Definitions in Section 4 slightly altered following suggestion of referee. Definitions in Sections 5 and 6 explained in more detail for clarity. Appendix adde