Joint IAS/PU Arithmetic Geometry
Algebraic de Rham Cohomology in Mixed Characteristic
I will discuss new structural properties of the de Rham cohomology of smooth schemes over the ring of Witt vectors. The main technical input is the $F$-gauge structure on crystalline cohomology. First, I will explain the slope obstruction to the injectivity of the de Rham-to-crystalline comparison morphism. This yields a negative answer to a question posed by Esnault–Kisin–Petrov. On the positive side, I will show that the comparison morphism becomes injective when restricted to suitable subspaces defined by slope conditions. Finally, I will illustrate how these techniques allow us to determine the de Rham cohomology modulo torsion for such schemes. This is joint work with Daniel Caro.
Date & Time
April 13, 2026 | 3:30pm – 4:30pm
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04/13/2026 15:30
04/13/2026 16:30
Joint IAS/PU Arithmetic Geometry
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Topic: Algebraic de Rham Cohomology in Mixed Characteristic
Speakers: Marco D'Adezzio, IRMA
More: https://www.ias.edu/math/events/joint-iaspu-arithmetic-geometry-50
I will discuss new structural properties of the de Rham cohomology of
smooth schemes over the ring of Witt vectors. The main technical input
is the $F$-gauge structure on crystalline cohomology. First, I will
explain the slope obstruction to the injectivity of the de
Rham-to-crystalline comparison morphism. This yields a negative answer
to a question posed by Esnault–Kisin–Petrov. On the positive side,
I will show that the comparison morphism becomes injective when
restricted to suitable subspaces defined by slope conditions. Finally,
I will illustrate how these techniques allow us to determine the de
Rham cohomology modulo torsion for such schemes. This is joint work
with Daniel Caro.
Princeton University, Fine Hall 224
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Location
Princeton University, Fine Hall 224Speakers
Marco D'Adezzio, IRMA