activity
20172026
most citedGeometrically irreducible -adic local systems are de Rham up to a twist

9 citations · 18 across the 8 of their papers we have counts for

collaborators

8 papers

math.AG2026

Formality for rigid-analytic spaces satisfying the weight-monodromy conjecture

Alexander Petrov, Bogdan Zavyalov

We prove that étale and de Rham cohomology algebras of a smooth proper rigid-analytic space over a finite extension of are formal if the rigid-analytic space satisfi…

math.AG2023★ 2 cited

Non-decomposability of the de Rham complex and non-semisimplicity of the Sen operator

Alexander Petrov

We describe the obstruction to decomposing in degrees the de Rham complex of a smooth variety over a perfect field of characteristic that lifts over , and…

math.NT2021

Universality of the Galois action on the fundamental group of

Alexander Petrov

We prove that any semi-simple representation of the Galois group of a number field coming from geometry appears as a subquotient of the ring of regular functions on the pro-algebra…

math.AG2021★ 3 cited

Hodge numbers are not derived invariants in positive characteristic

Nicolas Addington, Daniel Bragg

We study a pair of Calabi-Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence D^b(X) = D^b(M), building on work of Gro…

math.AG2020★ 9 cited

Geometrically irreducible -adic local systems are de Rham up to a twist

Alexander Petrov

We prove that any geometrically irreducible -local system on a smooth algebraic variety over a -adic field becomes de Rham after a twist by a charac…

math.AG2020★ 2 cited

Rigid-analytic varieties with projective reduction violating Hodge symmetry

Alexander Petrov

We construct examples of smooth proper rigid-analytic varieties admitting formal model with projective special fiber and violating Hodge symmetry for cohomology in degrees …

math.AG2019★ 1 cited

On the periodic topological cyclic homology of DG categories in characteristic p

Alexander Petrov, Vadim Vologodsky

We prove that the -adically completed periodic topological cyclic homology of a DG category over a perfect field of characteristic is isomorphic to the (-adically c…

math.AG2017★ 1 cited

The Gauss-Manin connection on the periodic cyclic homology

Alexander Petrov, Dmitry Vaintrob, Vadim Vologodsky

It is expected that the periodic cyclic homology of a DG algebra over the field of complex numbers (and, more generally, the periodic cyclic homology of a DG category) carries a lo…