21,880 research outputs found
Chow groups of ind-schemes and extensions of Saito's filtration
Let be a field of characteristic zero and let be the category of
smooth and separated schemes over . For an ind-scheme (and more
generally for any presheaf of sets on ), we define its Chow groups
. We also introduce Chow groups
for a presheaf with transfers
on . Then, we show that we have natural isomorphisms of Chow
groups where is the
presheaf with transfers that associates to any the collection of
finite correspondences from to . Additionally, when , we show that Saito's filtration on the Chow groups of a smooth projective
scheme can be extended to the Chow groups and more
generally, to the Chow groups of an arbitrary presheaf of sets on . Similarly, there exists an extension of Saito's filtration to the Chow
groups of a presheaf with transfers on . Finally, when the
ind-scheme is ind-proper, we show that the isomorphism
is actually a filtered
isomorphism.Comment: Exposition improve
L-functions for holomorphic forms on GSp(4) x GL(2) and their special values
We provide an explicit integral representation for L-functions of pairs (F,g)
where F is a holomorphic genus 2 Siegel newform and g a holomorphic elliptic
newform, both of squarefree levels and of equal weights. When F,g have level
one, this was earlier known by the work of Furusawa. The extension is not
straightforward. Our methods involve precise double-coset and volume
computations as well as an explicit formula for the Bessel model for GSp(4) in
the Steinberg case; the latter is possibly of independent interest. We apply
our integral representation to prove an algebraicity result for a critical
special value of L(s, F \times g). This is in the spirit of known results on
critical values of triple product L-functions, also of degree 8, though there
are significant differences.Comment: 48 pages, typos corrected, some changes in Sections 6 and 7, other
minor change
Absolute convergence of the twisted Arthur-Selberg trace formula
We show that the distributions occurring in the geometric and spectral side
of the twisted Arthur-Selberg trace formula extend to non-compactly supported
test functions. The geometric assertion is modulo a hypothesis on root systems
proven when the group is split. The result extends the work of Finis-Lapid (and
M\"uller, spectral side) to the twisted setting. We use the absolute
convergence to give a geometric interpretation of sums of residues of certain
Rankin-Selberg L-functions.Comment: Accepted to be published in Mathematische Zeitschrift. Removed proof
of RCL for base change; Section 8 now requires Assumption 8.1. Also, minor
correction
Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses
We study the nonequlibrium state of heat conduction in a one-dimensional
system of hard point particles of unequal masses interacting through elastic
collisions. A BBGKY-type formulation is presented and some exact results are
obtained from it. Extensive numerical simulations for the two-mass problem
indicate that even for arbitrarily small mass differences, a nontrivial steady
state is obtained. This state exhibits local thermal equilibrium and has a
temperature profile in accordance with the predictions of kinetic theory. The
temperature jumps typically seen in such studies are shown to be finite-size
effects. The thermal conductivity appears to have a very slow divergence with
system size, different from that seen in most other systems.Comment: 5 pages, 4 figures, Accepted for publication in Phys. Rev. Let
Non-extensive Statistical Mechanics and Black Hole Entropy From Quantum Geometry
Using non-extensive statistical mechanics, the Bekenstein-Hawking area law is
obtained from microstates of black holes in loop quantum gravity, for arbitrary
real positive values of the Barbero-Immirzi parameter. The
arbitrariness of is encoded in the strength of the "bias" created in
the horizon microstates through the coupling with the quantum geometric fields
exterior to the horizon. An experimental determination of will fix
this coupling, leaving out the macroscopic area of the black hole to be the
only free quantity of the theory.Comment: 6 pages, published versio
Classifying subcategories and the spectrum of a locally noetherian category
Let be a locally noetherian Grothendieck category. In this
paper, we study subcategories of using subsets of the spectrum
. Along the way, we also develop results in local
algebra with respect to the category that we believe to be of
independent interest.Comment: 40 pages, some new results adde
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