…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)…

**(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.*
**(Ayoub) ****Over fields of characteristic zero, the Betti realization functor from compact motives to chain complexes is conservative**. *Perhaps 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.*
**(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.”*
**(Bhatt-Lurie) The K theory of commutative rings is left Kan extended from smooth -algebras. ***Wait what? Oh yes. **Also, the precursor to EHKSY II.*
**(Ananyevskiy-Druzihin) Rigidity in SH. ***Ever wondered the extent of Suslin’s Pic-divisibility arguments? Here’s one on crack – with frames.*
**(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.*
**(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.*
**(Wendt) Variations in on a theme of Mohan Kumar. ***From the evening maestro of Mittag-Leffler – a motivic interpretation of a simpler time.*
**(Hahn-Yuan) ****Structured splittings via the Beilinson-Drinfeld Grassmanian. ***Who put the affine Grassmanian into my manifold calculus?*
**(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. *

### Like this:

Like Loading...