Zero cycles with modulus and zero cycles on singular varieties

Given a smooth variety $X$ and an effective Cartier divisor $D \subset X$, we show that the cohomological Chow group of 0-cycles on the double of $X$ along $D$ has a canonical decomposition in terms of the Chow group of 0-cycles ${\rm CH}_0(X)$ and the Chow group of 0-cycles with modulus ${\rm CH}_0(X|D)$ on $X$. When $X$ is projective, we construct an Albanese variety with modulus and show that this is the universal regular quotient of ${\rm CH}_0(X|D)$. As a consequence of the above decomposition, we prove the Roitman torsion theorem for the 0-cycles with modulus. We show that ${\rm CH}_0(X|D)$ is torsion-free and there is an injective cycle class map ${\rm CH}_0(X|D) \hookrightarrow K_0(X,D)$ if $X$ is affine. For a smooth affine surface $X$, this is strengthened to show that $K_0(X,D)$ is an extension of ${\rm CH}_1(X|D)$ by ${\rm CH}_0(X|D)$.Comment: 62 pages. Final version to appear in Compositio Mat

A Search for Interstellar CH2_2D+^+

We report on a search for Interstellar CH2D+. Four transitions occur in easily accessible portions of the spectrum; we report on emission at the frequencies of these transitions toward high column density star-forming regions. While the observations can be interpreted as being consistent with a detection of the molecule, further observations will be needed to secure that identification. The CH2D+ rotational spectrum has not been measured to high accuracy. Lines are weak, as the dipole moment induced by the inclusion of deuterium in the molecule is small. Astronomical detection is favored by observations toward strongly deuterium-fractionated sources. However, enhanced deuteration is expected to be most significant at low temperatures. The sparseness of the available spectrum and the low excitation in regions of high fractionation make secure identification of CH2D+ difficult. Nonetheless, owing to the importance of CH3+ to interstellar chemistry, and the lack of rotational transitions of that molecule owing to its planar symmetric structure, a measure of its abundance would provide key data to astrochemical models.Comment: 2 pages, 1 figure, submitted to IAU Symposium 251, Organic Matte

Measurement of CH3_3D on Titan at Submillimeter Wavelengths

We present the first radio/submillimeter detection of monodeuterated methane (CH$_3$D) in Titan's atmosphere, using archival data from of the Atacama Large Millimeter/submillimeter Array (ALMA). The $J_K=2_1-1_1$ and $J_K=2_0-1_0$ transitions at 465.235 and 465.250 GHz ($\sim0.644$ mm) were measured at significance levels of $4.6\sigma$ and $5.7\sigma$, respectively. These two lines were modeled using the Non-linear optimal Estimator for MultivariatE spectral analySIS (NEMESIS) radiative transfer code to determine the disk-averaged CH$_3$D volume mixing ratio = $6.157\times10^{-6}$ in Titan's stratosphere (at altitudes $\gt130$ km). By comparison with the CH$_4$ vertical abundance profile measured by Cassini-Huygens mass spectrometry, the resulting value for D/H in CH$_4$ is $(1.033\pm0.081)\times10^{-4}$. This is consistent with previous ground-based and in-situ measurements from the Cassini-Huygens mission, though slightly lower than the average of the previous values. Additional CH$_3$D observations at higher spatial resolution will be required to determine a value truly comparable with the Cassini-Huygens CH$_4$ measurements, by measuring CH$_3$D with ALMA close to Titan's equator. In the post-Cassini era, spatially resolved observations of CH$_3$D with ALMA will enable the latitudinal distribution of methane to be determined, making this an important molecule for further studies.Comment: 9 pages, 4 figure

Measurement of the production of charm jets tagged with D0^{0} mesons in pp collisions at s\sqrt{s}= 7 TeV

The production of charm jets in proton-proton collisions at a center-of-mass energy of $\sqrt{s}=7$ TeV was measured with the ALICE detector at the CERN Large Hadron Collider. The measurement is based on a data sample corresponding to a total integrated luminosity of $6.23$ ${\rm nb}^{-1}$, collected using a minimum-bias trigger. Charm jets are identified by the presence of a D$^0$ meson among their constituents. The D$^0$ mesons are reconstructed from their hadronic decay D$^0\rightarrow$K$^{-}\pi^{+}$. The D$^0$-meson tagged jets are reconstructed using tracks of charged particles (track-based jets) with the anti-$k_{\mathrm{T}}$ algorithm in the jet transverse momentum range $5<p_{\rm{T,jet}}^{\mathrm{ch}}<30$ ${\rm GeV/}c$ and pseudorapidity $|\eta_{\rm jet}|<0.5$. The fraction of charged jets containing a D$^0$-meson increases with $p_{\rm{T,jet}}^{\rm{ch}}$ from $0.042 \pm 0.004\, \mathrm{(stat)} \pm 0.006\, \mathrm{(syst)}$ to $0.080 \pm 0.009\, \rm{(stat)} \pm 0.008\, \rm{(syst)}$. The distribution of D$^0$-meson tagged jets as a function of the jet momentum fraction carried by the D$^0$ meson in the direction of the jet axis ($z_{||}^{\mathrm{ch}}$) is reported for two ranges of jet transverse momenta, $5<p_{\rm{T,jet}}^{\rm{ch}}<15$ ${\rm GeV/}c$ and $15<p_{\rm{T,jet}}^{\rm{ch}}<30$ ${\rm GeV/}c$ in the intervals $0.2<z_{||}^{\rm{ch}}<1.0$ and $0.4<z_{||}^{\rm{ch}}<1.0$, respectively. The data are compared with results from Monte Carlo event generators (PYTHIA 6, PYTHIA 8 and Herwig 7) and with a Next-to-Leading-Order perturbative Quantum Chromodynamics calculation, obtained with the POWHEG method and interfaced with PYTHIA 6 for the generation of the parton shower, fragmentation, hadronisation and underlying event.Comment: 29 pages, 8 captioned figures, 3 tables, authors from page 24, published version, figures at http://alice-publications.web.cern.ch/node/525

Tentative Detection of Deuterated Methane toward the Low-Mass Protostar IRAS 04368+2557 in L1527

The millimeter-wave rotational transition line ($J_K = 1_0 - 0_0$) of deuterated methane CH$_3$D has tentatively been detected toward the low-mass Class 0 protostar IRAS 04368+2557 in L1527 with the Heinrich Hertz Submillimeter Telescope. This is the first detection of CH$_3$D in interstellar clouds, if confirmed. The column density and fractional abundance of CH$_3$D are determined to be $(9.1\pm3.4) \times 10^{15}$ cm$^{-2}$ and $(3.0\pm1.1) \times 10^{-7}$, respectively, where we assume the rotational temperature of 25 K. The column density and fractional abundance of the gaseous CH$_4$ are estimated to be $(1.3-4.6) \times 10^{17}$ cm$^{-2}$ and $(4.3-15.2) \times 10^{-6}$, respectively, by adopting the molecular D/H ratios of 2--7% reported for various molecules in L1527. The fractional abundance of CH$_4$ is higher than or comparable to that found in high-mass star-forming cores by infrared observations. It is sufficiently high for triggering the efficient production of various carbon-chain molecules in a lukewarm region near the protostar, which supports the picture of the warm carbon-chain chemistry.Comment: 13 page

Algebraic cycles on Severi-Brauer schemes of prime degree over a curve

Let $k$ be a perfect field and let $p$ be a prime number different from the characteristic of $k$. Let $C$ be a smooth, projective and geometrically integral $k$-curve and let $X$ be a Severi-Brauer $C$-scheme of relative dimension $p-1$ . In this paper we show that $CH^{d}(X)_{{\rm{tors}}}$ contains a subgroup isomorphic to $CH_{0}(X/C)$ for every $d$ in the range $2\leq d\leq p$. We deduce that, if $k$ is a number field, then $CH^{d}(X)$ is finitely generated for every $d$ in the indicated range.Comment: 6 page