Beilinson regulator

E876106

arithmetic invariant cohomological construction regulator map

The Beilinson regulator is a deep arithmetic-geometric map connecting algebraic K-theory of varieties to their Deligne or absolute Hodge cohomology, playing a central role in conjectural formulas for special values of L-functions.

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Observed surface forms (1)

Surface form	Occurrences
Beilinson regulators	1

Statements (48)

Predicate	Object
instanceOf	arithmetic invariant ⓘ cohomological construction ⓘ regulator map ⓘ
appearsIn	Beilinson’s 1980s papers on higher regulators ⓘ literature on special values of L-functions ⓘ
appliesTo	motives over number fields ⓘ smooth algebraic varieties over number fields ⓘ
associatedWith	Deligne–Beilinson cohomology NERFINISHED ⓘ absolute Hodge cycles ⓘ mixed Hodge structures ⓘ motivic cohomology ⓘ
centralTo	Beilinson’s conjectural description of L-values ⓘ arithmetic of motives ⓘ
codomain	Deligne cohomology NERFINISHED ⓘ absolute Hodge cohomology NERFINISHED ⓘ
constructionUses	Deligne complexes NERFINISHED ⓘ differential forms with logarithmic singularities ⓘ higher Chow groups ⓘ
definedFor	K-groups of motives ⓘ K-groups of varieties over number fields ⓘ
domain	algebraic K-theory ⓘ higher K-groups ⓘ
field	algebraic K-theory ⓘ arithmetic geometry ⓘ number theory ⓘ
generalizes	Borel regulator NERFINISHED ⓘ Dirichlet regulator NERFINISHED ⓘ
hasRole	bridge between K-theory and cohomology theories ⓘ defines regulator maps in motivic cohomology ⓘ provides periods in conjectural L-value formulas ⓘ
motivates	development of motivic cohomology ⓘ study of absolute Hodge cohomology ⓘ
namedAfter	Alexander Beilinson NERFINISHED ⓘ
relatedConcept	higher regulators ⓘ periods of motives ⓘ polylogarithm motives ⓘ regulator map in algebraic K-theory ⓘ
relates	algebraic K-theory to Hodge-theoretic invariants ⓘ arithmetic geometry to complex geometry ⓘ
targetProperty	mixed Hodge structures with real structure ⓘ real Deligne cohomology groups ⓘ
usedIn	Beilinson conjectures on special values of L-functions NERFINISHED ⓘ Bloch–Kato conjectures NERFINISHED ⓘ Deligne’s conjectures on critical values of L-functions NERFINISHED ⓘ arithmetic of elliptic curves ⓘ arithmetic of modular forms ⓘ formulas for special values of motivic L-functions ⓘ study of motives ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Alexander Beilinson → knownFor → Beilinson regulator ⓘ

Deligne cohomology → relatedTo → Beilinson regulator ⓘ

this entity surface form: Beilinson regulators