Gems of 2017

…of which it’s been eventful – you know what I mean. In no particular order/nothing written by me (and apologies if your masterpiece isn’t included – I’m just a kid anyway)…

  1. (Nikolaus-Scholze;Ayala-Mazel-Gee-Rozenblyum) Ushering Topological Cyclic Homology into the 21st century. Well these papers deserve their hype – a homotopy invariant treatment of TC, with no recourse to the evil of models.
  2. (Ayoub) Over fields of characteristic zero, the Betti realization functor from compact motives to chain complexes is conservativePerhaps the next great achievement from the theory of motives after Voevodsky’s solution of Bloch-Kato/Milnor. Also half the standard conjectures – Grothendieck’s dream is alive and well.
  3. (Bachmann-Hoyois) Norms in motivic homotopy theory. A unified treatment of norms for K-theory, Chow groups and construction for algebraic cobordism and its cousins; the beginnings of a “motivic higher algebra.”
  4. (Bhatt-Lurie) The K theory of commutative rings is left Kan extended from smooth \mathbb{Z}-algebras. Wait what? Oh yes. Also, the precursor to EHKSY II.
  5. (Ananyevskiy-Druzihin) Rigidity in SH. Ever wondered the extent of Suslin’s Pic-divisibility arguments? Here’s one on crack – with frames.
  6. (Röndigs-Spitzweck-Østvær) The homotopy limit problem for hermitian K-theory via slices. Divide and conquer? More like slice and conquer. Brought to you by the unfair slice technology.
  7. (Levine) The theory of virtual fundamental classes. In my younger days this was fiction – now we know what the gods wanted to associate every closed subvariety with.
  8. (Wendt) Variations in \mathbb{A}^1 on a theme of Mohan KumarFrom the evening maestro of Mittag-Leffler – a motivic interpretation of a simpler time.
  9. (Hahn-Yuan) Structured splittings via the Beilinson-Drinfeld Grassmanian. Who put the affine Grassmanian into my manifold calculus?
  10. (Mirkovic-Vilonen) The geometric Satake isomorphism. I know this one is a classic – but it’s definitely new to me and infinitely inspiring and exciting like – you know – a teenage crush.