Do you want to publish a course? Click here

Arithmetic of Ch^atelet surface bundles revisited

69   0   0.0 ( 0 )
 Added by Yongqi Liang
 Publication date 2021
  fields
and research's language is English
 Authors Yongqi Liang




Ask ChatGPT about the research

We study arithmetic of the algebraic varieties defined over number fields by applying Lagrange interpolation to fibrations. Assuming a conjecture of M. Stoll, we show, for Ch^atelet surface bundles over curves, that the violation of Hasse principle being accounted for by the Brauer-Manin obstruction is not invariant under an arbitrary finite extension of the ground field.



rate research

Read More

Let T -> S be a finite flat morphism of degree two between regular integral schemes of dimension at most two (and with 2 invertible), having regular branch divisor D. We establish a bijection between Azumaya quaternion algebras on T and quadric surface bundles over S with simple degeneration along D. This is a manifestation of the exceptional isomorphism A_1^2 = D_2 degenerating to the exceptional isomorphism A_1 = B_1. In one direction, the even Clifford algebra yields the map. In the other direction, we show that the classical algebra norm functor can be uniquely extended over the discriminant divisor. Along the way, we study the orthogonal group schemes, which are smooth yet nonreductive, of quadratic forms with simple degeneration. Finally, we provide two surprising applications: constructing counter-examples to the local-global principle for isotropy, with respect to discrete valuations, of quadratic forms over surfaces; and a new proof of the global Torelli theorem for very general cubic fourfolds containing a plane.
109 - Huayi Chen 2021
We establish an arithmetic intersection theory in the framework of Arakelov geometry over adelic curves. To each projective scheme over an adelic curve, we associate a multi-homogenous form on the group of adelic Cartier divisors, which can be written as an integral of local intersection numbers along the adelic curve. The integrability of the local intersection number is justified by using the theory of resultants.
89 - Xinwen Zhu 2018
We survey some recent work on the geometric Satake of p-adic groups and its applications to some arithmetic problems of Shimura varieties. We reformulate a few constructions appeared in the previous works more conceptually.
We study indigenous bundles in characteristic p>0 with nilpotent p-curvature, and show that they correspond to so-called deformation data. Using this equivalence, we translate the existence problem for deformation data into the existence of polynomial solutions of certain differential equations with additional properties. As in application, we show that P^1 minus four points is hyperbolically ordinary (in the sense of Mochizuki. We also give a concrete application to existence of deformation data with fixed local invariants.
221 - Eugen Hellmann 2010
We consider stacks of filtered phi-modules over rigid analytic spaces and adic spaces. We show that these modules parametrize p-adic Galois representations of the absolute Galois group of a p-adic field with varying coefficients over an open substack containing all classical points. Further we study a period morphism (defined by Pappas and Rapoport) from a stack parametrizing integral data and determine the image of this morphism.
comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا