We define two decreasing filtrations by ramification groups on the absolute Galois group of a complete discrete valuation field whose residue field may not be perfect. In the classical case where the residue field is perfect, we recover the classical upper numbering filtration. The definition uses rigid geometry and log-structures. We also establish some of their properties.

We define the characteristic cycle of anétale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by Beilinson. We prove a formulaà la Milnor for the total dimension of the space of vanishing cycles and an index formula computing the Euler-Poincaré characteristic, generalizing the Grothendieck-Ogg-Shafarevich formula to higher dimension.An essential ingredient of the construction and the proof is a partial generalization to higher dimension of the semi-continuity of the Swan conductor due to Deligne-Laumon. We prove the index formula by establishing certain functorial properties of characteristic cycles.

Double differential cross sections between 0 • -12 • were measured for the 90 Zr(n, p) reaction at 293 MeV over a wide excitation energy range of 0-70 MeV. A multipole decomposition technique was applied to the present data as well as the previously obtained 90 Zr(p, n) data to extract the Gamow-Teller (GT) component from the continuum. The GT quenching factor Q was derived by using the obtained total GT strengths. The result is Q = 0.88 ± 0.06, not including an overall normalization uncertainty in the GT unit cross section of 16%.The (p, n) reaction at intermediate energies (T p > 100 MeV) provides a highly selective probe of spin-isospin excitations in nuclei due to the energy dependence of the isovector part of nucleon-nucleon (NN ) t-matrices [1]. The

In [6], S. Bloch conjectures a formula for the Artin conductor of the -adic etale cohomology of a regular model of a variety over a local field and proves it for a curve. The formula, which we call the conductor formula of Bloch, enables us to compute the conductor that measures the wild ramification by using the sheaf of differential 1-forms. In this paper, we prove the formula in arbitrary dimension under the assumption that the reduced closed fiber has normal crossings.

For a variety over a local field, we show that the alternating sum of the trace of the composition of the actions of an element of the Weil group and an algebraic correspondence on the ℓ-adic etale cohomology is independent of ℓ. We prove the independence by establishing basic properties of weight spectral sequences [15]. Let K be a complete discrete valuation field with finite residue field F of order q. We call such a field a local field. The geometric Frobenius F r F is the inverse of the map a → a q in the absolute Galois group G F = Gal(F /F). The Weil group W K is defined as the inverse image of the subgroup F r F ⊂ G F by the canonical map G K = Gal(K/K) → G F. For a scheme X K of finite type over K, the ℓ-adic etale cohomology H r (XK , Q ℓ) is a ℓ-adic representation of the absolute Galois group G K. For σ ∈ G K , the right action σ * on XK = X ⊗ KK induces the left action σ * = (σ *) * on H r (XK , Q ℓ).

In the analysis of background events from a counter-technique experiment to study cosmic-ray nuclei above 8-GV rigidity, two events were observed which are consistent with the assumption of Z--14, ,4-350, and 450 MeV/nucleon and which cannot be accounted for by more conventional background. Such events may be explained by the hypothesis of strange-quark matter (SQM). It is concluded that the existence of SQM has not been excluded by experiment at a flux level of ~6 x 10 ~9 cm ~2s ~' sr ~'. 12.38.Mh, 98.70.Sa There have been studies' of properties of strongly interacting matter in bulk. Witten 2 has proposed the possibility that matter consisting of a roughly equal number of up, down, and strange quarks may be stable at zero temperature and pressure. Stable strange matter has been studied by several authors 3 on the basis of the MIT bag model. The strange matter created in the early Universe would have evaporated and could not survive to the present time. 4 Possible sources of the strange matter would be in the collision of neutron stars, or in neutron stars with a superdense quark surface and in quark stars with thin nucleon envelopes. 5 If strange-quark matter is really stable, it must be an abundant component in cosmic radiation. On the other hand, Bjorken and McLerran 6 have sketched a hypothesis that the "Centauro" events 7 were caused by the explosion of a glob of highly dense matter. If the Centauro events are of a cosmic origin and they are accelerated with a mechanism similar to that for cosmic rays, they should be detected at the top of the atmosphere.Have existing direct experiments ruled out the scenario for the existence of cosmic quark matter or placed a certain restriction on the scenario? Along this line, we analyzed again the cosmic-ray data which were obtained with a counter telescope in 1981, and found a new type of event in galactic cosmic rays. Figure 1 shows a schematic view of an instrument, consisting of an acrylic Cherenkov counter (C, two channels C\ and Ci) and a scintillation counter (5, two channels S\ and S2) for measuring the primary charges with an accuracy of 0.35 unit of charges, a liquid Cherenkov counter of fluorocarbon (L, four channels L\, Li, £3, and L4) for measuring the particle energies around cutoff rigidities (10 GV) and two pairs of X-Y crossed multitube proportional counters 8 (MTPCs) for determining particle trajectories within an accuracy of 0.5 cm for single-particle as well as multiple tracks. For vertically incident carbon nuclei, about 195 photoelectrons were collected with the four combined 5-in. photomultiplier tubes (per channel) from the acrylate Cherenkov counter and about 35 photoelectrons with the three combined photomultiplier tubes (per channel) from the liquid Cherenkov counter. The geometric factor of this instrument is 6049 cm 2 sr and the total payload weighs 291 kg. It was flown in September 1981 from Sanriku Ballon Center, Japan. The instrument was rotating at 1 rpm in order to measure arrival directions of particles. Triggering by a coincidenc...

Link to this article: http://journals.cambridge.org/abstract_S1474748008000364How to cite this article: Takeshi Saito (2009). Wild ramication and the characteristic cycle of an ℓ-adic sheaf.Abstract We propose a geometric method to measure the wild ramification of a smoothétale sheaf along the boundary. Using the method, we study the graded quotients of the logarithmic ramification groups of a local field of characteristic p > 0 with arbitrary residue field. We also define the characteristic cycle of an -adic sheaf, satisfying certain conditions, as a cycle on the logarithmic cotangent bundle and prove that the intersection with the 0-section computes the characteristic class, and hence the Euler number.. Wild ramification and the characteristic cycle of an -adic sheaf 777Proof .(1) Let n 1 be an integer such that m = nr is an integer. Then, P (r)We show the inclusion is an equality. It suffices to show that l 0 m −[lr] K

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