Thesis

Some model-theoretical and geometric properties of fields with jet operators, PhD thesis, Wrocław University, April 2001, dvi or ps or pdf

Papers

  1. Stable Groups and Algebraic Groups, J. London Math. Soc. (1) 61 (2000), 51-57, doi: 10.1112/S0024610799008261, pdf
  2. (with Anand Pillay) Proalgebraic and differential algebraic group structures on affine spaces, Amer. J. Math. 122 (2000), 213-221, doi: 10.1353/ajm.2000.0004, pdf
  3. (with Marcin Chałupnik) Lazard's Theorem for differential algebraic and proalgebraic groups, Pacific J. Math. (2) 202 (2002), 305-312, doi: 10.2140/pjm.2002.202.305, pdf
  4. (with Anand Pillay) A Note on Groups Definable in Difference Fields, Proc. of AMS (1) 130 (2002), 205-212, doi: 10.1090/S0002-9939-01-06004-X, pdf
  5. Derivations of the Frobenius map, Journal of Symbolic Logic, (1) 70 (2005), 99-110, doi: 10.2178/jsl/1107298512, pdf
  6. Geometric axioms for existentially closed Hasse fields, Annals of Pure and Applied Logic, 135 (2005), 286-302, doi: 10.1016/j.apal.2005.02.003, pdf
  7. Jet operators on fields, Journal of Algebra, 289 (2005), 312-319, doi: 10.1016/j.jalgebra.2004.11.012, pdf
  8. (with Anand Pillay) Quantifier elimination for algebraic D-groups, Transactions AMS, 358 (2006) 167-181, doi: 10.1090/S0002-9947-05-03820-1, pdf
  9. (with Anand Pillay) On algebraic sigma-groups, Transactions AMS, 359 (2007) 1325-1337, doi: 10.1090/S0002-9947-06-04312-1, pdf
  10. (with Assaf Hasson) Strongly minimal expansions of (C,+) definable in o-minimal fields, Proc. London Math. Soc., (1) 97 (2008), 117-154, doi: 10.1112/plms/pdm052, pdf
  11. A note on a theorem of Ax, Annals of Pure and Applied Logic, 156 (2008), 96-109, doi: 10.1016/j.apal.2008.06.011, pdf
  12. Schanuel property for additive power series, Israel Journal of Mathematics, (1) 190 (2012), 349-363, doi: 10.1007/s11856-011-0178-2, pdf
  13. (with Anand Pillay) On the isotriviality of projective iterative delta-varieties, Journal of Pure and Applied Algebra, (1) 216 (2012), 20-27, doi: 10.1016/j.jpaa.2011.02.020, pdf
  14. (with Daniel Hoffmann) Integrating Hasse-Schmidt derivations, Journal of Pure and Applied Algebra (4) 219 (2015), 875-896, doi: 10.1016/j.jpaa.2014.05.024, pdf
  15. (with Daniel Hoffmann) A note on extending actions of infinitesimal group schemes, Journal of Algebra, 446 (2016), 275-290, doi: 10.1016/j.jalgebra.2015.08.031, pdf
  16. (with Daniel Hoffmann) Existentially closed fields with G-derivations, J. London Math. Soc. (3) 93 (2016), 590-618, doi: 10.1112/jlms/jdw009, pdf
  17. (with Serge Randriambololona) Strongly minimal reducts of valued fields, Journal of Symbolic Logic, (2) 81 (2016), 510-523, doi: 10.1017/jsl.2015.61, pdf
  18. Ax-Schanuel condition in arbitrary characteristic, to appear in Journal of the Institute of Mathematics of Jussieu, doi: 10.1017/S1474748017000378, pdf
  19. (with Daniel Hoffmann) Existentially closed fields with finite group actions, accepted to Journal of Mathematical Logic, pdf
  20. (with Marcin Chałupnik) Difference modules and difference cohomology, submitted, pdf
  21. (with Özlem Beyarslan) Model Theory of Fields with Virtually Free Group Actions, submitted, pdf

Preprints and Notes not intended for formal publication

  1. (with Anand Pillay) Subvarieties of commutative meromorphic groups, pdf
  2. Homological algebra (mini-lecture notes), pdf
  3. Algebraic curves (lecture notes), pdf
  4. Model theory (Şirince summer school mini-lecture notes), pdf

Slides from talks

  1. Strongly minimal sets definable in expansions of RCF (joint work with A. Hasson), o-minimal conference, Leeds, March 2006; seminar talk, Regensburg, June 2006.
  2. Definability in Differential Fields, Logic Colloquium 2007, Wrocław, 14-19 July.
  3. Iterative D-varieties via group scheme actions (joint work with A. Pillay), Atelier MODNET de Théorie des Modèles des corps, Luminy (France), 12-16 November 2007.
  4. Independence in positive characteristic, Geometric Model Theory, a conference in honour of Boris Zilber, in celebration of his 60th birthday; Oxford, March 2010.
  5. Transcendence in positive characteristic, Model Theory Conference in Seoul, May 2010.
  6. Unlikely formal intersections, Workshop Interactions of model theory with number theory and algebraic geometry, MPIM Bonn (Germany), June 2012.
  7. Model Theory of Fields with Operators, Tutorial at PhD's in Logic VIII, Darmstadt (Germany), 9-11 May 2016.
  8. Difference algebra and generic rational cohomology (joint work with M. Chałupnik), Workshop on Interactions between Model Theory and Arithmetic Dynamics, The Fields Institute, Toronto (Canada), 25-29 July 2016.
  9. Model theory of Galois actions (joint work with Ö. Beyarslan) Differential Galois Theory and Differential Algebraic Groups, The Fields Institute, Toronto (Canada), 24-28 July 2017.

Wersja polska

English version