Analysis on arithmetic schemes. II

DOI10.1017/is010004028jkt103zbMath1225.14019OpenAlexW2482574726WikidataQ56566813 ScholiaQ56566813MaRDI QIDQ3580643

I. B. Fesenko

Publication date: 13 August 2010

Published in: Journal of K-theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/is010004028jkt103

zbMATH Keywords

zeta functionzeta integraltwo-dimensional adelic analysisTate's thesishigher class field theoryelliptic curve over global fieldtopological Milnor K-groups

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Arithmetic algebraic geometry (Diophantine geometry) (11G99) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Miscellaneous applications of (K)-theory (19M05) Cycles and subschemes (14C99) Generalized class field theory ((K)-theoretic aspects) (19F05)

Related Items

Geometric and analytic structures on the higher adèles ⋮ Anabelian group-theoretic properties of the absolute Galois groups of discrete valuation fields ⋮ Adelic geometry on arithmetic surfaces. I: Idelic and adelic interpretation of the Deligne pairing ⋮ Mean-periodicity and zeta functions ⋮ Generalised Kawada-Satake method for Mackey functors in class field theory ⋮ Geometric two‐dimensional idèles with cycle module coefficients ⋮ Positivity of certain functions associated with analysis on elliptic surfaces ⋮ Locally convex structures on higher local fields ⋮ Zeta integrals on arithmetic surfaces ⋮ Adelic geometry on arithmetic surfaces. II: Completed adeles and idelic Arakelov intersection theory ⋮ Ramification of higher local fields, approaches and questions

Cites Work

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• Fourier transform over local fields
• Integration on valuation fields over local fields
• De Rham cohomology and conductors of curves
• Fourier transformat, constants of the functional equations and Weil conjecture
• Invariant subspaces in the theory of operators and theory of functions
• On the Riemann-Roch theorem for orders in the ring of valuation vectors of a function field
• Residues and adeles
• Representations of algebraic groups over a 2-dimensional local field
• Residues and differential operators on schemes
• Unramified class field theory of arithmetical surfaces
• The value ring of geometric motivic integration, and the Iwahori Hecke algebra of \(\text{SL}_2\). With an appendix by Nir Avni.
• On elliptic modular surfaces
• On the ideal structure of some algebras of analytic functions
• Zeta functions of simple algebras
• Some Examples of Hecke Algebras for Two-Dimensional Local Fields
• Higher algebraic K-theory: I
• Spherical Hecke algebras of SL 2 over 2-dimensional local fields
• On the Rationality of the Zeta Function of an Algebraic Variety