The Strong Franchetta Conjecture in Arbitrary Characteristics
نویسندگان
چکیده
Using Moriwaki’s calculation of the Q-Picard group for the moduli space of curves, I prove the strong Franchetta Conjecture in all characteristics. That is, the canonical class generates the group of rational points on the Picard scheme for the generic curve of genus g ≥ 3. Similar results hold for generic pointed curves.
منابع مشابه
$L_1$-Biharmonic Hypersurfaces in Euclidean Spaces with Three Distinct Principal Curvatures
Chen's biharmonic conjecture is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we consider an advanced version of the conjecture, replacing $Delta$ by its extension, $L_1$-operator ($L_1$-conjecture). The $L_1$-conjecture states that any $L_1$-biharmonic Euclidean hypersurface is 1-minimal. We prove that the $L_1$-conje...
متن کاملStark’s Question and a Strong Form of Brumer’s Conjecture
We show that a question posed by Stark in 1980, regarding abelian L– functions of order of vanishing 2 at s = 0, has a negative answer in the case of characteristic p global fields. We provide links between various versions of Stark’s question and a strong form of Brumer’s Conjecture, in the general context of global fields of arbitrary characteristic. As a consequence, we show that the strong ...
متن کاملFrankl's Conjecture for a subclass of semimodular lattices
In this paper, we prove Frankl's Conjecture for an upper semimodular lattice $L$ such that $|J(L)setminus A(L)| leq 3$, where $J(L)$ and $A(L)$ are the set of join-irreducible elements and the set of atoms respectively. It is known that the class of planar lattices is contained in the class of dismantlable lattices and the class of dismantlable lattices is contained in the class of lattices ha...
متن کاملThe Rubin–stark Conjecture for a Special Class of Function Field Extensions
We prove a strong form of the Brumer–Stark Conjecture and, as a consequence, a strong form of Rubin’s integral refinement of the abelian Stark Conjecture, for a large class of abelian extensions of an arbitrary characteristic p global field k. This class includes all the abelian extensions K/k contained in the compositum kp∞ := kp · k∞ of the maximal pro-p abelian extension kp/k and the maximal...
متن کاملDetermination of an Effective Wedge Angle by Combination of Two Arbitrary Universal Wedge Fields in Radiation Therapy of Cancer Patients with Megavoltage Photon Beams.
Introduction: Wedge filters are commonly used in radiation oncology for eliminating hot spots and creating a uniform dose distribution in optimizing isodose curves in the target volume for clinical aspects. These are some limited standard physical wedges (15°, 30°, 45°, 60°), or creating an arbitrary wedge angle, like motorized wedge or dynamic wedge, ... The new formulation is...
متن کامل