We prove that, modulo any power of a prime $ p $, the absolute integral closure of an
excellent noetherian domain is Cohen-Macaulay. A graded analog is also established …

Let $ X $ be an integral scheme of finite type over a complete DVR of mixed characteristic.
We provide a definition of a test ideal which agrees with the multiplier ideal after inverting …

We prove a uniform bound on the growth of symbolic powers of arbitrary (not necessarily
radical) ideals in arbitrary (not necessarily excellent) regular rings of all characteristics. This …

Algebraic geometry in mixed characteristic Page 1 Algebraic geometry in mixed characteristic
Bhargav Bhatt Abstract Fix a prime number p. We report on some recent developments in …

We prove that, given a sufficiently functorial assignment from rings to big Cohen-Macaulay
algebras $ R\mapsto B $, that the associated big Cohen-Macaulay closure operation on …

We present an effective global generation result for direct images of pluricanonical bundles
in mixed characteristic. This is a mixed characteristic analog of Ejiri's theorem in positive …

Let X be a smooth projective variety over a complete discretely valued field of mixed
characteristic. We solve non-archimedean Monge-Amp\ere equations on X assuming …

In this paper, we use big Cohen-Macaulay algebras to define a characteristic free analog of
the $ F $-thresholds, which we call BCM-thresholds, in the case of principal ideals. We prove …

We give short, closure-theoretic proofs for uniform bounds on the growth of symbolic powers
of ideals in regular rings. The author recently proved these bounds in mixed characteristic …

Although Kodaira vanishing is only available in characteristic zero, Bhatt [BM+ 23] proved a
Kodaira-type vanishing theorem “up to finite covers”. Bhatt's vanishing theorem is employed …