9 citations · 32 across the 21 of their papers we have counts for
26 papers
Algebraic independence of the exponential and Weierstrass -functions
Cristiana Bertolin
Let be a lattice in with algebraic invariants and complex multiplication, let be the elliptic curve associated with , and let be the Weierst…
Dimension of the motivic Galois group of a 1-motive
Cristiana Bertolin
We compute the dimension of the motivic Galois group of a 1-motive M defined over the field of complex numbers, expressing it explicitly in terms of the rank of the multiplicative…
1-motives and admissible variations of mixed Hodge structures
Cristiana Bertolin
Let S be a connected scheme smooth and of finite type over the field of complex numbers. To every 1-motive over S, André associated the enriched Hodge realization given by a torsio…
A conjecture in Schanuel style for 1-motives
Cristiana Bertolin
Schanuel Conjecture contains all ``reasonable" statements that can be made on the values of the exponential function. In particular it implies the Lindemann-Weierstrass Theorem. In…
Variations on Schanuel's Conjecture for elliptic and quasi-elliptic functions I: the split case
Cristiana Bertolin, Michel Waldschmidt
It is expected that Schanuel's Conjecture contains all ``reasonable" statements that can be made on the values of {\em the exponential function}. In particular it implies the Linde…
The group law of Picard stacks via matrices
Cristiana Bertolin, Federica Galluzzi
Let S be a site. We show that the 2-stack of strictly commutative Picard stacks over S is algebraic, i.e. it is 2-equivalent to the 2-stack of 2-algebras for an adequate algebraic…
Mumford-Tate groups of 1-motives and Weil pairing
Cristiana Bertolin, Patrice Philippon
We show how the geometry of a 1-motive (that is existence of endomorphisms and relations between the points defining it) determines the dimension of its motivic Galois group ${…
Semi-abelian analogues of Schanuel Conjecture and applications
Cristiana Bertolin, Patrice Philippon, Biswajyoti Saha +1
In this article we study Semi-abelian analogues of Schanuel conjecture. As showed by the first author, Schanuel Conjecture is equivalent to the Generalized Period Conjecture applie…
Third kind elliptic integrals and 1-motives
Cristiana Bertolin
In our PH.D. thesis we have showed that the Generalized Grothendieck's Conjecture of Periods applied to 1-motives, whose underlying semi-abelian variety is a product of elliptic cu…
A note on divisorial correspondences of extensions of abelian schemes by tori
Cristiana Bertolin, Federica Galluzzi
Let S be a locally noetherian scheme and consider two extensions G_1 and G_2 of abelian S-schemes by S-tori. In this note we prove that the fppf-sheaf Corr _S(G_1,G_2) of divisoria…
Brauer groups of 1-motives
Cristiana Bertolin, Federica Galluzzi
Over a normal base scheme, we prove the generalized Theorem of the Cube for 1-motives and that a torsion class of the group H^2_ét(M,G_m)$ of a 1-motive M, whose pull-back via the…
Morphisms of 1-motives defined by line bundles
Cristiana Bertolin, Sylvain Brochard
Let be a normal base scheme. The aim of this paper is to study the line bundles on 1-motives defined over . We first compute a dévissage of the Picard group of a 1-motive $M…
Higher-dimensional study of extensions via torsors
Cristiana Bertolin, Ahmet Emin Tatar
Let S be a site. First we define the 3-category of torsors under a Picard S-2-stack and we compute its homotopy groups. Using calculus of fractions we define also a pure algebraic…
Extensions of Picard 2-Stacks and the cohomology groups Ext^i of length 3 complexes
Cristiana Bertolin, Ahmet Emin Tatar
The aim of this paper is to define and study the 3-category of extensions of Picard 2-stacks over a site S and to furnish a geometrical description of the cohomology groups Ext^i o…
Biextensions of Picard stacks and their homological interpretation
Cristiana Bertolin
Let S be a site. We introduce the 2-category of biextensions of strictly commutative Picard S-stacks. We define the pull-back, the push-down, and the sum of such biextensions and w…
Extensions and biextensions of locally constant group schemes, tori and abelian schemes
Cristiana Bertolin
Let S be a scheme. We compute explicitly the group of homomorphisms, the S-sheaf of homomorphisms, the group of extensions, and the S-sheaf of extensions involving locally constant…
Extensions of Picard stacks and their homological interpretation
Cristiana Bertolin
Let S be a site. We introduce the notion of extensions of strictly commutative Picard S-stacks. We define the pull-back, the push-down, and the sum of such extensions and we comput…
Deligne's conjecture on extensions of 1-motives
Cristiana Bertolin
We introduce the notion of extension of 1-motives. Using the dictionary between strictly commutative Picard stacks and complexes of abelian sheaves concentrated in degrees -1 and 0…
Biextensions of 1-motives in Voevodsky's category of motives
Cristiana Bertolin, Carlo Mazza
Let k be a perfect field. In this paper we prove that biextensions of 1-motives define multilinear morphisms between 1-motives in Voevodsky's triangulated category of effective geo…
Homological interpretation of extensions and biextensions of 1-motives
Cristiana Bertolin
Let k be a separably closed field. Let K_i=[A_i \to B_i] (for i=1,2,3) be three 1-motives defined over k. We define the geometrical notions of extension of K_1 by K_3 and of biexte…
Some tensor products
Cristiana Bertolin
We define the tensor product of 1-motives with motives of weight 0 and we construct explicitely the 1-motive underlying the quotient M_1 \otimes M_2 / W_{-3}(M_1 \otimes M_2).
Multilinear morphisms between 1-motives
Cristiana Bertolin
Let S be an arbitrary scheme. We define biextensions of 1-motives by 1-motives which we see as the geometrical origin of morphisms from the tensor product of two 1-motives to a thi…
Some motivic pairings
Cristiana Bertolin
In this note we prove the geometrical origin of pairings of abelian schemes. According to Deligne's philosophy of motives, this means that these pairings are motivic. We make also…
Realizations of Biextensions
Cristiana Bertolin
Let k be a field of characteristic 0 and M(k) is the category of 1-motives over k. We prove that Biext^1(M_1,M_2;M_3)=Hom_{MR(k)}(T(M_1)\otimes T(M_2), T(M_3))