arXiv math/00121522000-12-18math.NTmath.AG

Invitation to higher local fields, Part II, section 2: Adelic constructions for direct images of differentials and symbols

Denis Osipov

备注：: For introduction and notation, see math.NT/0012131 . Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon3/m3-II-2.abs.html
发表信息：: Geom. Topol. Monogr. Volume 3(2000) 215-221

英文摘要：

This work introduces adelic constructions of direct images of differentials and symbols in the two-dimensional case in the relative situation. In particular, reciprocity laws for relative residues of differentials and symbols are stated and applied to a construction of the Gysin map for Chow groups.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Invitation to higher local fields, Part II, section 1: Higher dimensional local fields and L-functions

This work describes several first steps in extending Tate-Iwasawa's analytic method to define an L-function in higher dimensions. For generalizing this method the author advocates the usefulness of the classical Riemann-Hecke approach, his adelic complexes together with his generalization of Krichever's correspondence. He analyzes dimension 1 types of functions and discusses properties of the lattice of commensurable classes of subspaces in the adelic space associated to a divisor on an algebraic surface.

2000-12-18math.AGmath.NT

Invitation to higher local fields, Part I, section 8: Explicit formulas for the Hilbert symbol

This is a review of the vast area of explicit formulas for the (wild) Hilbert symbol (not only in the one-dimensional case but in the higher dimensional case as well). An extensive bilbiography is included.

2001-02-13math.AGmath.NT

Invitation to higher local fields, Part I, section 4: Cohomological symbol for henselian discrete valuation fields of mixed characteristic

This is a sketch of main steps of the proof of Bloch--Kato's theorem which states that the norm residue homomorphism K_q(K)/m\to H^q(K,\Bbb Z/m(q)) is an isomorphism for a henselian discrete valuation field K of characteristic 0 with residue field of positive characteristic.

2000-12-18math.AGmath.NT

Invitation to higher local fields, Part I, section 10: Explicit higher local class field theory

This is a presentation of explicit methods to construct higher local class field theory by using topological K-groups, explicit symbols and a generalization of Neukirch-Hazewinkel's axiomatic approaches. The existence theorem is discussed as well.

2000-12-18math.AGmath.NT

Invitation to higher local fields, Part II, section 6: Phi-Gamma-modules and Galois cohomology

This is is a survey of applications of Fontaine's theory of p-adic representations of local fields (Phi-Gamma-modules) to Galois cohomology of local fields and explicit formulas for the Hilbert symbol in relation with two-dimensional local objects.

2000-12-18math.AGmath.NT

Invitation to higher local fields, Part I, section A: Appendix to Section 2

This appendix discusses some basic definitions and properties of differential forms and Kato's cohomology groups in characteristic p and a sketch of the proof of Bloch-Kato-Gabber's theorem which describes the differential symbol from the Milnor K-group K_n(F)/p of a field F of positive characteristic p to the differential module Ω_F^n.

2000-12-18math.ACmath.AGmath.NT

更多相关论文收起更多论文

Central extensions and reciprocity laws on algebraic surfaces

We consider an algebraic surface. For an irreducible curve on this surface and for a point on this curve one can associate an artinian ring, which is a sum of two-dimensional local fields. An example of two-dimensional local field is iterated Laurent series. We consider an integer value symbol on a two-dimensional local field. This symbol appears for the description of non-ramified coverings of two-dimensional local fields and for the description of intersection index of divisors on surfaces by adeles. We interpret this symbol as the commutator of lifting of elements in the central extension o…

2005-01-21math.AGmath.NT