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Singular homology of arithmetic schemes
 Algebra Number Theory
"... Abstract: We construct a singular homology theory on the category of schemes of finite type over a Dedekind domain and verify several basic properties. For arithmetic schemes we construct a reciprocity isomorphism between the integral singular homology in degree zero and the abelianized modified ta ..."
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Cited by 13 (5 self)
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Abstract: We construct a singular homology theory on the category of schemes of finite type over a Dedekind domain and verify several basic properties. For arithmetic schemes we construct a reciprocity isomorphism between the integral singular homology in degree zero and the abelianized modified
Tame coverings of arithmetic schemes
"... The objective of this paper is to investigate tame fundamental groups of schemes of finite type over Spec(Z). More precisely, let X be a connected scheme of finite type over Spec(Z) and letX be a compactification of X, i.e. a scheme which is proper and of finite type over Spec(Z) and which contains ..."
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fields and we show that a finite covering of a regular arithmetic scheme with nilpotent Galois group is tamely ramified if and only if all associated extensions of higher dimensional henselian fields are tame. Then we use this fact in the proof of the following Theorem 1 Let X be a regular and connected
Analysis on Arithmetic Schemes. I
 DOCUMENTA MATH.
, 2003
"... A shift invariant measure on a two dimensional local field, taking values in formal power series over reals, is introduced and discussed. Relevant elements of analysis, including analytic duality, are developed. As a two dimensional local generalization of the works of Tate and Iwasawa a local zeta ..."
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Cited by 22 (4 self)
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A shift invariant measure on a two dimensional local field, taking values in formal power series over reals, is introduced and discussed. Relevant elements of analysis, including analytic duality, are developed. As a two dimensional local generalization of the works of Tate and Iwasawa a local zeta integral on the topological Milnor K t 2group of the field is introduced and its properties are studied.
Smallness of fundamental groups for arithmetic schemes
, 2008
"... The smallness is proved of fundamental groups for arithmetic schemes. This is a higher dimensional analogue of the HermiteMinkowski theorem. We also refer to the case of varieties over finite fields. As an application, we consider the finiteness of representations of the fundamental groups over alg ..."
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Cited by 2 (1 self)
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The smallness is proved of fundamental groups for arithmetic schemes. This is a higher dimensional analogue of the HermiteMinkowski theorem. We also refer to the case of varieties over finite fields. As an application, we consider the finiteness of representations of the fundamental groups over
Étale duality for constructible sheaves on arithmetic schemes
"... In this note we relate the following three topics for arithmetic schemes: a general duality for étale constructible torsion sheaves, a theory of étale homology, and the arithmetic complexes of GerstenBlochOgus type defined by K. Kato [KCT]. In brief, there is an absolute duality using certain dual ..."
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Cited by 13 (3 self)
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In this note we relate the following three topics for arithmetic schemes: a general duality for étale constructible torsion sheaves, a theory of étale homology, and the arithmetic complexes of GerstenBlochOgus type defined by K. Kato [KCT]. In brief, there is an absolute duality using certain
Tame class field theory for arithmetic schemes
, 2004
"... The aim of global class field theory is the description of abelian extensions of a finitely generated field k in terms of its arithmetic invariants. The solution of this problem in the case of fields of dimension 1 was one of the major achievements of number theory in the first part of the previous ..."
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Cited by 4 (4 self)
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The aim of global class field theory is the description of abelian extensions of a finitely generated field k in terms of its arithmetic invariants. The solution of this problem in the case of fields of dimension 1 was one of the major achievements of number theory in the first part of the previous
A composite arithmetic scheme for the evaluation of multinomials
 In Proc. of the 38th Asilomar Conference on Signals, Systems and Computers
, 2004
"... Abstract: We discuss the implementation aspects ..."
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