Duality of Albanese and Picard 1‐motives

Ramachandran, Niranjan

doi:10.1023/a:1011100812900

Cited by 28 publications

(34 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For such a U a natural object to consider is the generalised Albanese variety Alb U defined by Serre [24]: it is a semi-abelian variety equipped with a morphism U → Alb U universal for morphisms of U into semi-abelian varieties that send a fixed base point to 0. According to [25] (see also [21]) the dual of the 1-…”

Section: Theorem 02 Let K Be a Number Field And M A 1-motive Over Kmentioning

confidence: 99%

Arithmetic Duality Theorems for 1-Motives

Harari¹,

Szamuely²

2005

Journal Fur Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

Section: Theorem 02 Let K Be a Number Field And M A 1-motive Over Kmentioning

confidence: 99%

Arithmetic Duality Theorems for 1-Motives

Harari¹,

Szamuely²

2005

Journal Fur Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

“…Let Pic + (V ) := Pic + (X · , Y · ) be the Picard 1-motive of V (see Section 5 and Appendix A, cf. [2] and [22]). In the same way, as de Jong suggested in [6, p. 51-52], we set H * crys (V · /W(k)) := H * logcrys (X · , Y · ) where (X · , Y · ) here denotes the simplicial logarithmic structure on X · determined by Y · (see Section 6).…”

Section: The Resultsmentioning

confidence: 99%

Crystalline realizations of 1-motives

Andreatta

Barbieri-Viale

2004

Math. Ann.

View full text Add to dashboard Cite

We consider the crystalline realization of Deligne's 1-motives in positive characteristics and prove a comparison theorem with the De Rham realization of (formal) liftings to zero characteristic.We then show that one dimensional crystalline cohomology of an algebraic variety, defined by forcing universal cohomological descent via de Jong's alterations, coincides with the crystalline realization of the Picard 1-motive, over perfect fields of cahracteristic > 2.

show abstract

“…The map α is the universal homomorphism of Z X to sheaves represented by group varieties of which the connected component containing zero is a (semi-)abelian variety (see for example [Ra,§1]). We will call Alb * (X) the total Albanese variety of X .…”

Section: Picard and Albanese Varietymentioning

confidence: 99%

Lichtenbaum-Tate duality for varieties over p-adic fields

Hamel¹

2004

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

ABSTRACT. S. Lichtenbaum has proved in [L1] that there is a nondegenerate pairingbetween the Picard group and the Brauer group of a nonsingular projective curve C over a p -adic field K (a finite extension of the p -adic numbers Q p ). On the level of divisors the pairing is induced by the norm map Br(K ) → Br(K) for finite extensions K /K . The nondegeneracy is proven by a reduction to Tate duality for commutative group schemes over p -adic fields. This reduction is achieved by explicit cocycle calculations in Galois cohomology. The present paper introduces a new homology theory, pseudo-motivic homology, which allows us to reconstruct the above duality as a purely formal combination of a generalised form of Tate duality over p -adic fields and a form of Poincaré duality for curves over arbitrary fields due to P. Deligne. This gives a more conceptual proof of Lichtenbaum's result and an analogue in higher dimensions.

show abstract

Duality of Albanese and Picard 1‐motives

Cited by 28 publications

References 29 publications

Arithmetic Duality Theorems for 1-Motives

Arithmetic Duality Theorems for 1-Motives

Crystalline realizations of 1-motives

Lichtenbaum-Tate duality for varieties over p-adic fields

Contact Info

Product

Resources

About