Kazim Buyukboduk's Research Page



My research is supported by an IRC Advanced Laureate Award. (press release)



My investigations lie in the realm of Number Theory, Arithmetic Algebraic Geometry, and the arithmetic aspects of the Langlands Programme.

Very roughly speaking, my research concerns Galois representations (that come attached to automorphic forms), algebraic cycles on the relevant Shimura varieties, and Euler systems (in their various incarnations), which I often study from an Iwasawa theoretic view point -- recently, with an emphasis on critical points on eigenvarieties.

You may find below a list of my math writings (and where they appeared, when applicable).

 

                                               
 

     
 

 

   


 

 
     
                                                                
I co-organize the UCD Algebra and Number Theory Seminar.
Here is a link to its schedule.
Please drop me a line if you are swinging by Dublin and wish to speak at our seminar.


I organised a satellite conference to Journees Arithmetiques XXXI. Here is a link to its page.

                                                                                                                                          
Publications:
  1. (w/ Denis Benois) Arithmetic of critical p-adic L-functions. Video-1 Video-2 Oberwolfach report
    Memoirs of the AMS (to appear).
  2. (w/ A. Lei)  Iwasawa theory of twists of elliptic modular forms over imaginary quadratic fields at inert primes.
    Memoires de la Societe Mathematique de France (to appear).
  3. (w/ A. Burungale and A. Lei) Anticyclotomic Iwasawa theory of abelian varieties of GL2-type at non-ordinary primes.
    Adv. Math. 439 (2024), Paper No. 109465, 63 pp.
  4. (w/ T. Ochiai) Main conjectures for higher rank nearly ordinary families -- I.
    J. Number Theory 252 (2023), 1--73.
  5. (w/ R. Sakamoto) ℒ-Invariants, p-Adic Heights, and Factorization of p-Adic L-Functions.
    IMRN (2023) Vol. 2023, Issue 4, 2867--2943 DOI: 10.1093/imrn/rnab322
  6. (w/ D. Benois) On the exceptional zeros of p-non-ordinary p-adic L-functions and a conjecture of Perrin-Riou.
    Transactions of the AMS 376 (2023), Number 1, pp. 231--284.
  7. (w/ R. Sakamoto) On the non-critical exceptional zeros of Katz p-adic L-functions for CM fields.
    Adv. Math. 406 (2022), Paper No. 108478, 54 pp.
  8. (w/ A. Lei) Iwasawa theory for GL2 x ResK/QGL1
    Ann. Math. Que. 46 (2022), no. 2, 347--418 (Special birthday issue for Bernadette Perrin-Riou).
  9. (w/ Denis Benois) Interpolation of Beilinson-Kato elements and p-adic L-functions.
    Ann. Math. Que. 46 (2022), no. 2, 231--287 (Special birthday issue for Bernadette Perrin-Riou).
  10. (w/ A. Lei) Interpolation of Generalized Heegner Cycles in Coleman Families.
    J. Lond. Math. Soc. (2) 104 (2021), no. 4, 1682--1716. DOI: 10.1112/jlms.12471
  11. (w/ A. Lei) Iwasawa theory of elliptic modular forms over imaginary quadratic fields at non-ordinary primes. Video
    IMRN (2021) Vol. 2021, Issue 14, 10654--10730 DOI: 10.1093/imrn/rnz117
  12. (w/ A. Lei and G. Venkat) Iwasawa theory for symmetric square of p-non-ordinary eigenforms.
    Doc. Math. 26 (2021), 1--63.
  13. (w/ A. Lei) Functional Equation for p-adic Rankin-Selberg L-functions.
    Ann. Math. Que. 44 (2020), no. 1, 9--25.
  14. Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and the Perrin-Riou Conjecture. Development of Iwasawa Theory -- the Centennial of K. Iwasawa's Birth. Advanced Studies in Pure Mathematics, 2020: 141--193 (2020).
  15. (w/ A. Lei) Rank-2 Euler systems for symmetric squares.
    Trans. Amer. Math. Soc. 372 (2019), no. 12, 8605--8619.
  16. (w/ A. Lei, D. Loeffler and G. Venkat) Iwasawa theory for Rankin--Selberg products of p-non-ordinary eigenforms.
    Algebra & Number Theory 13(4), 2019, 901--941.
  17. (w/ A. Lei) Anticyclotomic p-ordinary Iwasawa Theory of Elliptic Modular Forms.
    Forum Mathematicum 30 (2018), no. 4, 887--913. Video
  18. On the Iwasawa theory of CM fields for supersingular primes.  
    Trans. Amer. Math. Soc. 370 (2018), no. 2, 927--966.
  19. p-adic variation in arithmetic geometry: a survey.
    Algebraic geometry and number theory, 1--27, Progr. Math., 321, Birkhauser/Springer, Cham, 2017.
  20. (w/ A. Lei) Integral Iwasawa Theory of Galois Representations for non-ordinary primes.
    Math. Z. 286 (2017), no. 1-2, 361--398.
  21. Deformations of Kolyvagin systems. 
    Ann. des Sciences Math. du Quebec, Vol. 40 (2016), no. 2, 251-302     (Special Issue on the Occasion of Glenn Stevens' 60th Birthday)
  22. On Nekovar's heights, exceptional zeros and a conjecture of Mazur-Tate-Teitelbaum.
    IMRN (2016) Vol. 2016 2197--2237 doi:10.1093/imrn/rnv205
  23. (w/ A. Lei) Coleman-adapted Rubin-Stark Kolyvagin systems and supersingular Iwasawa theory of CM abelian varieties.  
    Proceedings of the London Mathematical Society (3) 111 (2015), no. 6, 1338--1378.
  24. On the anticyclotomic Iwasawa theory of CM forms at supersingular primes 
     Rev. Mat. Ibero., 31 (2015), no. 1, 109--126.
  25. Main conjectures for CM fields and a Yager-type theorem for Rubin-Stark elements.
    IMRN (2014), no. 21, 5832--5873.
  26. Big Heegner point Kolyvagin system for a family of modular forms.
    Selecta Math., 20 (3) (2014), 787--815.
  27. Height pairings, Exceptional zeros and Rubin's formula.
    Comment. Math. Helv. 87 (2012), no. 1, 71--111.
  28. Stickelberger elements and Kolyvagin systems.
    Nagoya Math. J. 203 (2011), 123--173.
  29. Λ-adic Kolyvagin systems.
    IMRN, (2011) Vol. 2011 3141--3206 doi:10.1093/imrn/rnq186
  30. On Euler systems of rank r and their Kolyvagin systems.
    Indiana University Math. Journal, 59 (2010),  1277--1332
  31. Kolyvagin systems of Stark units.
    Journal fuer die Reine und Angewandte Mathematik, 631 (2009), 85--107.
  32. Stark units and the main conjectures for totally real fields.
    Compositio Math. 145(5), 1163--1195 (2009).
  33. Tamagawa defect of Euler systems.
    Journal of Number Theory 129 (2009) 402--417.

Preprints:

  1. (w/ A. Burungale and A. Lei) Anticyclotomic Iwasawa theory of abelian varieties of GL2-type at non-ordinary primes II.
  2. (w/ D. Casazza and R. Sakamoto) On the Artin formalism for p-adic Garrett--Rankin L-functions.
  3. (w/ R. Pollack and S. Sasaki) p-adic Gross--Zagier formula at critical slope and a conjecture of Perrin-Riou -- I.


Last Update: March 2024