1,720,991 research outputs found
Remarks on 1-motivic sheaves
No full textWe generalize the construction of the category of 1-motives with torsion M due to Barbieri-Viale, Rosenschon and Saito, as well as the construction of the category of 1-motivic sheaves Shv due to Barbieri-Viale and Kahn to perfect fields k (without inverting the exponential characteristic). For k transcendental over the prime field we extend showing that M and Shv have equivalent bounded derived categories
Formal Néron models and Weil restriction
No full textIt is known that in algebraic geometry the Néron model (if it exists) of a smooth group scheme G over a local field K can be recovered using the Weil restriction functor from the Néron model of the extension of G to a finite field extension of K. We extends the classical results to the context of formal Neron models of rigid group schemes
On perfectness of Grothendieck's pairing for the l-parts of component groups
No full textWe prove the perfectness of Grothendieck's pairing on l-parts of component groups of an abelian variety and its dual when l is prime to the residue characteristic. We show that this pairing differs in sign from another perfect pairing introduced by Grothendieck
Deligne's duality for de Rham realizations of 1-motives
No full textWe show that the pairing on de Rham realizations of 1-motives in "Theorie di Hodge III", IHES 44, can be defined over any base scheme and we prove that it gives rise to a perfect duality if one is working with a 1-motive and its Cartier dual. Furthermore we study universal extensions of 1-motives and their relation with natural-extensions
ALGEBRA
No full textQuest'opera è una traduzione da un libro di successo, originariamente pubblicato in tedesco. Si tratta di un libro di testo per studenti di che seguono il corso di algebra. Ogni capitolo presenta in modo sistematico la teoria e introduce alle problematiche della materia. Al termine di ogni sezione si trova una ricca varietà di esercizi; inoltre, in appendice sono riportati suggerimenti per risolvere alcuni esercizi. Sebbene sia pensato per i corsi del primo biennio, il volume contiene sezioni utili anche per seminari o corsi avanzati
Local flat duality of abelian varieties
No full textLet K be a field complete for a discrete valuation and with algebraically closed residue field of positive characteristic p. We prove the existence of a non-degenerate pairing between the first (flat) cohomology group of an abelian variety A over K and the fundamental group of the Néron model of the dual abelian variety. This pairing extends to the p-primary components a pairing introduced by Shafarevich. We relate this
pairing with Grothendieck’s pairing
Sharp de Rham realization
No full textReview dei risultati noti sulla realizzazione di de Rham di 1-motivi, della sharp de Rham realizzazione degli 1-motivi con parte additivia. Confronto con le strutture di Hodge formali introdotte da Barbieri-Viale
Il funtore di restrizione di Weil nel contesto della Geometria rigido-formale
No full textContiene un breve report sui risultati della tesi di dottorato relativi al comportamento del funtore di restrizione di Weil nel contesto della geometria rigida e della geometria formale
Remarks on 1–motivic sheaves.
No full textWe generalize the construction of the category of 1–motives with torsion tM_1, by Barbieri-Viale, Rosenschon and Saito, as well as the construction of the category of 1–motivic sheaves Shv_1, by Barbieri-Viale and Kahn,to perfect fields k (without inverting the exponential characteristic). For k transcendental over the prime field we extend a result of Barbieri-Viale and Kahn in showing that tM_1 and Shv_1 have equivalent bounded derived categories
Generalized 1-motivic sheaves
No full textLet k be a field of characteristic 0. We extend the definition of the category of 1-motivic sheaves, introduced by Barbieri-Viale and Kahn, allowing quotients of connected algebraic k-groups by formal k-groups. We show that its bounded derived category is equivalent to the bounded derived category of the category of generalized 1-motives with torsion
- …
