7 papers · 1 filter
Ramified periods and field of definition
Giuseppe Ancona, Dragoş Frăţilă, Alberto Vezzani
Let be an extension of number fields that is ramified above . We give a new obstruction to the descent to of smooth projective varieties defined over . The obstruct…
An Artin--Mumford criterion for conic bundles in characteristic two
Emiliano Ambrosi, Giuseppe Ancona
We prove a characteristic two version of the famous criterion of Artin and Mumford for irrationality of conic bundles. On the one hand, combined with the pathological behaviour of…
Ngô support theorem and polarizability of quasi-projective commutative group schemes
Giuseppe Ancona, Dragos Fratila
We prove that any commutative group scheme over an arbitrary base scheme of finite type over a field with connected fibers and admitting a relatively ample line bundle is polarizab…
Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations
Giuseppe Ancona, Mattia Cavicchi, Robert Laterveer +1
We show that the hyper-Kähler varieties of OG10-type constructed by Laza-Saccà-Voisin (LSV) verify the Lefschetz standard conjecture. This is an application of a more general resul…
Standard conjectures for abelian fourfolds
Giuseppe Ancona
Let A be an abelian fourfold. We prove the Standard Conjecture of Hodge type for A. By combining this result with a theorem of Clozel we deduce that numerical equivalence on A coin…
Conservativity of realizations on motives of abelian type over finite fields
Giuseppe Ancona
We show that the l-adic realization functor is conservative when restricted to the Chow motives of abelian type over a finite field. A weak version of this conservativity result ex…