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Everything about Local field
Locally compact infinite topological field
In mathematics, a local field is a locally compact Hausdorff non-discrete topological field. Local fields find many applications in algebraic number theory, where they arise naturally as completions of global fields. Moreover, tools like integration and Fourier analysis are available for functions defined on local fields. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Local fieldA 5-minute orientation
- Skim a recent paper: SERS-Based Local Field Enhancement in Biosensing ApplicationsInfluential work since 2022
- Pick up a classic book: Corps locauxThe most-reprinted book on the subject
- Read the landmark paper: Local light field fusionCited 1,218 times
- Go sideways: Adele ringA closely related topic
- Go sideways: Idele groupA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Local light field fusion
How Local Is the Local Field Potential?
The local Galactic magnetic field
Magnetism and Local Molecular Field
Local field theory for solitons
Local field potential
Visualizing local vector field topology
Impact of local electrostatic field rearrangement on field ionization
🆕 Influential since 2022
SERS-Based Local Field Enhancement in Biosensing Applications
Unusual local electric field concentration in multilayer ceramic capacitors
Recent Progress on Local Field Manipulations of Graphene Photodetectors
Twin-Field Quantum Key Distribution with Local Frequency Reference
Local Characterization of Field Emission Properties of Graphene Flowers
📚 Books worth reading
Corps locauxJean-Pierre Serre · 1962
Local algebraJean-Pierre Serre · 1965- 📕Analysis in positive characteristicAnatoly N. Kochubei · 2009
- 📕To an effective local Langlands correspondenceColin J. Bushnell · 2014
Locally convex spaces over non-Archimedean valued fieldsC. Perez-Garcia · 2009- 📕Public transit access to major league ballparksInstitute of Transportation Engineers · 2007
- 📕Proceedings of a Conference on Local FieldsConference on Local Fields (1966 Driebergen, Netherlands) · 1967
Localclass field theoryKenkichi Iwasawa · 1986
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Adele ring In number theory, the adele ring is a construction that combines all local versions of a global field into one object. For the rational numbers, these…
- Idele group In number theory, the idele group is a way of packaging the multiplicative arithmetic of a global field at all of its completions at once, so that it contains…
- Discrete valuation ring In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal. This means a DVR is an…
- Conductor (class field theory) In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification in…
- Valuation ring In abstract algebra, a valuation ring is an integral domain D such that for every non-zero element x of its field of fractions F, at least one of x or…
- Integral element In commutative algebra, an element b of a commutative ring B is said to be integral over a subring A of B if b is a root of some monic polynomial over…
- Spectrum of a ring In mathematics, and more specifically in commutative algebra and algebraic geometry, the prime spectrum (or simply the spectrum) of a commutative ring…
- Order (ring theory) In mathematics, certain subsets of some fields are called orders. The set of integers is an order in the rational numbers (the only one). In an algebraic…