Tom Bachmann

Contact

Work in preparation

• Motivic spectral mackey functors
• Mod 2 Power Operations in Normed Motivic Spectra

Preprints

• (with Marc Hoyois) Remarks on étale motivic stable homotopy theory [arxiv]
• (with Elden Elmanto and Jeremiah Heller) Motivic colimits and extended powers [arxiv]
• (with Paul Arne Østvær) Topological models for stable motivic invariants of regular number rings [arxiv]
• (with Adeel A. Khan, Charanya Ravi and Vladimir Sosnilo) Categorical Milnor squares and K-theory of algebraic stacks [arxiv]
• Eta-periodic motivic stable homotopy theory over Dedekind domanis [arxiv]
• (with Mike Hopkins) Eta-periodic motivic stable homotopy theory over fields [arxiv]
• (with Elden Elmanto and Paul Arne Østvær) Stable motivic invariants are eventually étale local [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 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

• Algebraic K-theory from the viewpoint of motivic homotopy theory [pdf]
• (with Elden Elmanto) Notes on motivic infinite loop space theory [arxiv]
• A1-invariants in Galois cohomology and a claim of Morel [arxiv]
• Part III essay: Homological Mirror Symmetry for Elliptic Curves [pdf]

Teaching

SS 2021: Algebraic Geometry 2, Galois Cohomology

WS 2020/1: Algebraic Geometry 1

Fall 2019: 18.904

Spring 2019: 18.906