The u-invariant of the function fields of p-adic curves

The u-invariant of a field is the maximum dimension of ansiotropic quadratic forms over the field. It is an open question whether the u-invariant of function fields of p-aidc curves is 8. In this paper, we answer this question in the affirmative for function fields of non-dyadic p-adic curves.Comment: 20 page

Failure of the local-global principle for isotropy of quadratic forms over rational function fields

We prove the failure of the local-global principle, with respect to all discrete valuations, for isotropy of quadratic forms over a rational function field of transcendence degree at least 2 over the complex numbers. Our construction involves the generalized Kummer varieties considered by Borcea and Cynk--Hulek.Comment: 7 pages, comments welcome

Area spectrum and thermodynamics of KS black holes in Ho\v{r}ava gravity

We investigate the area spectrum of Kehagias-Sfetsos black hole in Ho\v{r}ava-Lifshitz gravity via modified adiabatic invariant $I=\oint p_i d q_i$ and Bohr-Sommerfeld quantization rule. We find that the area spectrum is equally spaced with a spacing of $\Delta A=4 \pi l_p ^2$. We have also studied the thermodynamic behavior of KS black hole by deriving different thermodynamic quantities.Comment: 9 pages, 3 figures. Gen Relativ Gravit 201