Rational and integral points on Markoff-type K3 surfaces
Speaker: Dao Quang Duc
Time: 9:30 -- 11: 00, April 16, 2025
Venue: Room 612, A6, Institute of Mathematics-VAST
Abstract: Following a recent work of Fuchs, Litman, Silverman, and Tran on Markoff-type K3 (MK3) surfaces, we study the local-global principle for integral points on these surfaces. In particular, we construct a family of MK3 surfaces with infinitely many rational points but no integral points due to the Brauer–Manin obstruction, and give some counting results of a similar nature to those in recent works of Ghosh and Sarnak; Loughran and Mitankin; and Colliot-Thélène, Wei, and Xu. We also give results on the computation of geometric Picard groups and algebraic Brauer groups of MK3 surfaces in this family.
Related Seminars
- Symbolic Dynamics and Graph Algebras
- Additive actions and local algebras: the Hassett-Tschinkel correspondence
- Linear cores of graded algebras (Part II)
- Multiple zeta values and their algebraic structure
- Linear cores of graded algebras
- Exact Structures on Monomorphism Categories
- The v-number of generalized binomial edge ideals of some graphs
- Brill-Noether theory on curves from generic to specific
- Inc-Compatible Term Orders and Gröbner Theory in Infinitely Many Variables
- Exploration of the exponential sum over primes and over sums of two squares
Featured News
View all
Upcoming Conferences
View allNew Publications
View allInstitute Lectures
View allSpeaker: Claude Sabbah (CNRS, École Polytechnique, Institut Polytechnique de Paris, France)