Preprints
- Strongly A^1-invariant sheaves (after F. Morel) [arxiv]
- (with Robert Burklund)
E-infinity coalgebras and p-adic homotopy theory [arxiv] - A C_2-equivariant Gabber presentation lemma
[arxiv] - (with Aravind Asok and Mike Hopkins)
On P^1-stabilization in unstable motivic homotopy theory
[arxiv] - (with Elden Elmanto and Jeremiah Heller)
Splitting results for normed motivic spectra
[arxiv] - (with Elden Elmanto and Jeremiah Heller) Normed motivic spectra and power operations [arxiv]
- (with Aravind Asok and Mike Hopkins)
On the Whitehead theorem for nilpotent motivic spaces
[arxiv]
Motivic spectral Mackey functors
[arxiv]- (with Marc Hoyois)
Remarks on étale motivic stable homotopy theory
[arxiv] - (with Elden Elmanto and Jeremiah Heller)
Motivic colimits and extended powers
[arxiv] - (with Mike Hopkins) Eta-periodic motivic stable homotopy theory over fields [arxiv]
- (with Jeremy Hahn) Nilpotence in normed MGL-modules [arxiv]
- (with Jean Fasel) On the effectivity of spectra representing motivic cohomology theories [arxiv]
Publications
- (with Kirsten Wickelgren)
On quadratically enriched excess and residual intersections
[Crelle] [arxiv] - (with Elden Elmanto and Paul Arne Østvær)
Stable motivic invariants are eventually étale local [JEMS] [arxiv] - Motivic stable homotopy theory is strictly commutative at the characteristic [AiM] [arxiv]
- (with Adeel A. Khan, Charanya Ravi and Vladimir Sosnilo)
Categorical Milnor squares and K-theory of algebraic stacks [Selecta] [arxiv]
The very effective covers of KO and KGL over Dedekind schemes
[JEMS] [arxiv]- Eta-periodic motivic stable homotopy theory over Dedekind domanis [Journal of Topology] [arxiv]
- (with Paul Arne Østvær)
Topological models for stable motivic invariants of regular number rings [Forum Math. Sigma] [arxiv] - (with Hana Jia Kong, Guozhen Wang and Zhouli Xu)
The Chow t-structure on motivic spectra [Annals] [arxiv] - Cancellation theorem for motivic spaces with finite flat transfers [Documenta Math.] [arxiv]
- The zeroth P^1-stable homotopy sheaf of a motivic space [Jussieu] [arxiv]
- (with Elden Elmanto, Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson)
On the infinite loop spaces of algebraic cobordism and the motivic sphere [epiga] [arxiv] - (with Kirsten Wickelgren)
A^1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections [Jussieu] [arxiv] - (with Elden Elmanto)
Voevodsky's slice conjectures via Hilbert schemes [AG] [arxiv] - (with Maria Yakerson) Towards conservativity of Gm-stabilization [G&T] [arxiv]
- Rigidity in etale motivic stable homotopy theory [AGT] [arxiv]
- Motivic Tambara Functors [Math. Z.] [arxiv]
- (with Marc Hoyois) Norms in Motivic Homotopy Theory [Asterisque] [arxiv]
- Affine Grassmannians in A^1-algebraic Topology [Sel. Math.] [pdf] [arxiv]
- On the Conservativity of the Functor Assigning to a Motivic Spectrum its
Motive [Duke] [arxiv] - Motivic and Real Etale Stable Homotopy Theory [Compositio] [arxiv]
- (with Alexander Vishik) Motivic equivalence of affine quadrics [Math. Ann.] [arxiv]
- Some Remarks on Units in Grothendieck-Witt Rings [Journal of Algebra] [arxiv]
- The Generalized Slices of Hermitian K-Theory [Journal of Topology] [arxiv]
- On the Invertibility of Motives of Affine Quadrics [Documenta Math.] [arxiv]
Miscellaneous
Teaching
WS 2024/5: Foundations of Motivic Homotopy Theory, exercises: 1 2 3 4
SS 2024: Übungsaufgaben Quasikategorien 1, Übungsaufgaben Quasikategorien 2
WS 2023/4: Übungsaufgaben Steenrod-Operationen
Übungsaufgaben SSS
WS 2021/2: Algebraic Number Theory, Presheaves with transfer
SS 2021: Algebraic Geometry 2, Galois Cohomology
WS 2020/1: Algebraic Geometry 1
Fall 2019: 18.904
Spring 2019: 18.906
Impressum
Angaben gem. § 5 TMG:
Bachmann, Tom
Institut für Mathematik
Johannes Gutenberg-Universität
Staudingerweg 9
55128 Mainz
Kontaktaufnahme:
Telefon: +49 6131 39-28755
E-Mail: tom.bachmann@zoho.com