8,119 research outputs found
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
Entropy spectrum of (1+1) dimensional stringy black holes
We explore the entropy spectrum of dimensional dilatonic stringy
black holes via the adiabatic invariant integral method and the Bohr-Sommerfeld
quantization rule. It is found that the corresponding spectrum depends on black
hole parameters like charge, ADM mass and more interestingly on the dilatonic
field. We calculate the entropy of the present black hole system via the
Euclidean treatment of quantum gravity and study the thermodynamics of the
black hole and find that the system does not undergo any phase transition.Comment: 10 pages, 2 figure
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