Associate Professor James Borger
ANU College of Science
Areas of expertise
- Algebra And Number Theory 010101
- Category Theory, K Theory, Homological Algebra 010103
Publications
- Borger, J & Gurney, L 2020, 'Canonical lifts and δ-structures', Selecta Mathematica, vol. 26, no. 5, pp. 1-48.
- Borger, J & Gurney, L 2019, 'Canonical Lifts of Families of Elliptic Curves', Nagoya Mathematical Journal, vol. 233, pp. 193-213.
- Borger, J & Grinberg, D 2016, 'Boolean Witt vectors and an integral Edrei-Thoma theorem', Selecta Mathematica, vol. 22, no. 2, pp. 595-629.
- Borger, J 2016, 'Witt vectors, semirings, and total positivity', in Koen Thas (ed.), Absolute Arithmetic and �� Geometry, European Mathematical Society Publishing House, Germany, pp. 273-331pp.
- Borger, J 2011, 'The basic geometry of Witt vectors. II: Spaces', Mathematische Annalen, vol. 351, no. 4, pp. 877-933.
- Borger, J & Buium, A 2011, 'Differential forms on arithmetic jet spaces', Selecta Mathematica, vol. 17, no. 2, pp. 301-335.
- Borger, J 2011, 'The basic geometry of Witt vectors, I The affine case', Algebra & Number Theory, vol. 5, no. 2, pp. 231-285.
- Borger, J & de Smit, B 2008, 'Galois theory and integral models of Λ-rings', Bulletin of the London Mathematical Society, vol. 40, no. 3, pp. 436-446.
- Borger, J & Wieland, B 2005, 'Plethystic Algebra', Advances in Mathematics, vol. 194, pp. 246-283.
- Borger, J 2004, 'A monogenic Hasse-Arf theorem', Journal de Theorie des Nombres de Bordeaux, vol. 16, pp. 373-375.
- Borger, J 2004, 'Conductors and the moduli of residual perfection', Mathematische Annalen, vol. 329, pp. 1-30.
Projects and Grants
Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.
- Witt vectors and their applications in arithmetic algebraic geometry (Primary Investigator)
- Towards a concrete theory of cohomology: a fundamental concept in geometry (Primary Investigator)
- Big de Rham-Witt cohomology: towards a concrete theory of motives (Primary Investigator)
- Topological Lambda-Algebras (Primary Investigator)
