Imperial College London

Dr Oli Gregory

Faculty of Natural SciencesDepartment of Mathematics

Heilbronn Research Fellow







615Huxley BuildingSouth Kensington Campus





I am a research fellow working in arithmetic geometry. More precisely, I work on p-adic cohomology and p-adic Hodge theory, with applications to mixed/positive characteristic geometry and arithmetic conjectures on algebraic cycles/K-theory/motivic cohomology. 

Papers and preprints:

- O. Gregory, Motivic cohomology and K-theory of some surfaces over finite fields, J. Pure Appl. Algebra, 228 (2023), no. 4, Paper No. 107518, 21 pp.

- O. Gregory, Torsion codimension 2 cycles on supersingular abelian varieties, Canad. Math. Bull. 66 (2023), no. 2, 458-466. 

- O. Gregory, A. Langer, A log-motivic cohomology for semistable varieties and its p-adic deformation theory, submitted.

- O. Gregory, A. Langer, Hodge-Witt decomposition of relative crystalline cohomology, J. London Math. Soc., 106 (2022), 4009-4046.

- O. Gregory, Crystals of relative displays and Calabi-Yau threefolds, J. Number Theory, 237 (2022), 257-284.

- O. Gregory, A. Langer, Higher displays arising from filtered de Rham-Witt complexes, Arithmetic L-Functions and Differential Geometric Methods, 121–140, Progr. Math., 338, Birkhauser/Springer (2021).

- O. Gregory, A. Langer, Overconvergent de Rham-Witt cohomology for semistable varieties, Münster J. Math, no. 2, 541-571 (2020).

- O. Gregory, C. Liedtke, p-adic Tate conjectures and abeloid varieties, Doc. Math. 24, 1879-1934 (2019).

- O. Gregory, Crystals of relative displays and Grothendieck-Messing deformation theory, PhD thesis.

Other writing:

Here is my 2014 Cambridge Part III essay, Higher regulators of number fields, written under the supervision of Tony Scholl. It is an exposition of A. Borel's Cohomology de SL(n) et valeurs de fonctions zeta aux points entiers, Ann. Sc. Norm. Super. Pisa 4 (1977).


In November/December 2023, I taught an advanced LTCC course on Beilinson's Conjectures. I shall keep the lecture notes and exercise sheets available here. I urge you to take a look at Steven Landsburg's lovely answer to the MathOverflow question "What is the Beilinson regulator?".

Lecture 1. Motivic cohomology.

Lecture 2. Deligne cohomology and L-functions.

Lecture 3. Beilinson's conjectures

Lecture 4. Beilinson's conjectures for number fields (work of Borel and applications)

Lecture 5. The Bloch-Kato Tamagawa number conjecture 

Exercise Sheet 1

Exercise Sheet 2

Exercise Sheet 3

Exercise Sheet 4

Here is the exam for the course. The deadline is 14/01/2024. Please return your solutions to me by email.