• Benjamin Antieau, Daniel Bragg: Derived invariants from topological Hochschild homology is a really interesting paper, making tools and results from topological variations of Hochschild homology (and closely related invariants) accessible to algebraic geometers. I saw a great talk by the first author 2 days ago in Warsaw, and the paper is equally pleasant to read.

An important highlight is that a counterexample to the Hochschild–Kostant–Rosenberg decomposition in small characteristic is announced, to be given in a different paper. The only thing I've learnt about it so far is that it is a smooth projective approximation of the classifying stack $\mathrm{B}\mu_p$ but I am looking forward to learn more about it.

• Richard Nest, Boris Tsygan: Cyclic homology is a book-in-progress on cyclic homology (and other invariants, such as Hochschild (co)homology), for ($\mathrm{A}_\infty$-)algebras. It's already more than 200 pages, and promises to be an accessible read on some recent developments in the theory.