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).