Universal norms of -units in some non-commutative Galois extensions.
A Hasse principle for two dimensional global fields.
Duality theories for -primary etale cohomology II
Symmetric Bilinear Forms, Quadratic Forms and Milnor K-Theory in Characteristic Two.
The explicit reciprocity law and the cohomology of Fontaine-Messing
-adic etale cohomology
On the conductor formula of Bloch
In [6], S. Bloch conjectures a formula for the Artin conductor of the ℓ-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.
Albanese varieties with modulus and Hodge theory
Let be a proper smooth variety over a field of characteristic and an effective divisor on with multiplicity. We introduce a generalized Albanese variety Alb of of modulus , as higher dimensional analogue of the generalized Jacobian with modulus of Rosenlicht-Serre. Our construction is algebraic. For we give a Hodge theoretic description.
The GL2 main conjecture for elliptic curves without complex multiplication
Let G be a compact -adic Lie group, with no element of order , and having a closed normal subgroup H such that G/H is isomorphic to . We prove the existence of a canonical Ore set S of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient of M by its...
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