Overconvergent cohomology and quaternionic Darmon points

نویسندگان

  • Xavier Guitart
  • Marc Masdeu
چکیده

We develop the (co)homological tools that make effective the construction of the quaternionic Darmon points introduced by Matthew Greenberg. In addition, we use the overconvergent cohomology techniques of Pollack–Pollack to allow for the efficient calculation of such points. Finally, we provide the first numerical evidence supporting the conjectures on their rationality.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A comparison of logarithmic overconvergent de Rham-Witt and log-crystalline cohomology for projective smooth varieties with normal crossing divisor

In this note we derive for a smooth projective variety X with normal crossing divisor Z an integral comparison between the log-crystalline cohomology of the associated log-scheme and the logarithmic overconvergent de Rham-Witt cohomology defined by Matsuue. This extends our previous result that in the absence of a divisor Z the crystalline cohomology and overconvergent de Rham-Witt cohomology a...

متن کامل

Darmon’s points and quaternionic Shimura varieties

In this paper, we generalize a conjecture due to Darmon and Logan (see [DL03] and [Dar04], chapter 8) in an adelic setting. We study the relation between our construction and Kudla’s works on cycles on orthogonal Shimura varieties. This relation allows us to conjecture a Gross-Kohnen-Zagier theorem for Darmon’s points.

متن کامل

Cohomological descent on the overconvergent site

Background Cohomological descent is a robust computational and theoretical tool, central to p-adic cohomology and its applications. On the one hand, it facilitates explicit calculations (analogous to the computation of coherent cohomology in scheme theory via Čech cohomology); on the other, it allows one to deduce results about singular schemes (e.g., finiteness of the cohomology of overconverg...

متن کامل

Integral Monsky-washnitzer Cohomology and the Overconvergent De Rham-witt Complex

In their paper which introduced Monsky-Washnitzer cohomology, Monsky and Washnitzer described conditions under which the definition can be adapted to give integral cohomology groups. It seems to be well-known among experts that their construction always gives well-defined integral cohomology groups, but this fact also does not appear to be explicitly written down anywhere. In this paper, we pro...

متن کامل

On Base Change Theorem and Coherence in Rigid Cohomology

We prove that the base change theorem in rigid cohomology holds when the rigid cohomology sheaves both for the given morphism and for its base extension morphism are coherent. Applying this result, we give a condition under which the rigid cohomology of families becomes an overconvergent isocrystal. Finally, we establish generic coherence of rigid cohomology of proper smooth families under the ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. London Math. Society

دوره 90  شماره 

صفحات  -

تاریخ انتشار 2014