Livia Grammatica
Université de Strasbourg
livia.grammatica at math.unistra.fr
Talk to me in: it · fr · en · de
Livia Grammatica
Université de Strasbourg
livia.grammatica at math.unistra.fr
Talk to me in: it · fr · en · de
Welcome to my homepage! I am a second year PhD student at IRMA Strasbourg, working under the joint supervision of Marco D'Addezio (IRMA) and Anna Cadoret (IMJ-PRG). I am broadly interested in algebraic and arithmetic geometry, and my current research revolves around cohomology theories in positive characteristic, monodromy groups of isocrystals and Brauer groups.
Here is my extended CV. And here some places where I have been or will be in the future:
- 31 August to 4 September 2026 · Recent Developments in Arithmetic and Algebraic Geometry in Positive Characteristic, Wuppertal [†]
- 18-20 March 2026 · Recent Advances in Motivic Cohomology, Osnabrück [†]
- — — —
- 19-23 January 2026 · Motives in Montpellier [†]
- 3-28 November 2025 · Visit @ University of Regensburg
- 4-6 November 2025 · London Number Theory Seminar [†]
- 1-5 September 2025 · Period maps: classical and p-adic, Cargese [†]
- 23 April to 9 May 2025 · Arithmetic of K3 Surfaces, Lausanne [†]
Research
L.G., Alexei Skorobogatov, Yuan Yang, Brauer groups of abelian varieties over fields of finite characteristic (2025), preprint
We study the p-primary torsion of the Brauer group of an abelian variety over an algebraically closed field of characteristic p>0. The key part is an infinite group of finite p-exponent, which is naturally identified the group of k-points of some unipotent algebraic group. We determine the dimension of this unipotent group, find bounds for its p-exponent, and compute its full isogeny type in several cases. We wrote SageMath scripts (source code on GitHub) for quickly computing isogeny types.
L.G., Formal smoothness of the Artin–Mazur formal groups (2025), preprint
In this paper we establish cohomological criteria for the Artin-Mazur formal groups of X to be smooth, when X is a smooth proper variety over an algebraically closed field. We use them to construct, in characteristic 2 and for any d≥2, varieties X for which Фᵈ(X,𝔾ₘ) is representable but not formally smooth.
L.G., Some applications of the Nygaard filtration and quasisyntomic descent in positive characteristic (2025), preprint
This article gives an expository account of quasisyntomic descent and the Nygaard filtration in positive characteristic, complemented by some applications to p-adic cohomology theories. This is an expanded version of my master thesis.
Made with help from Marco Lastres ⟩<^,«·>