Publications (8)
Crystalline representations and Wach modules in the relative case II
Abhinandan
We study relative Wach modules generalising our previous works on this subject. Our main result shows a categorical equivalence between relative Wach modules and lattices inside re…
An integral comparison of crystalline and de Rham cohomology
Abhinandan, Alex Youcis
Let be a mixed characteristic complete DVR with perfect residue field and fraction field . It is a celebrated result of Berthelot and Ogus that for a smooth…
Crystalline representations and Wach modules in the relative case
Abhinandan
We study the notion of Wach modules in relative setting, generalizing the arithmetic case. Over an unramified base, for a -adic representation admitting such structure, we exami…
Syntomic complex and -adic nearby cycles
Abhinandan
In local relative -adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine-…
Prismatic -crystals and Wach modules
Abhinandan
We show that the category of analytic/completed prismatic -crystals on the absolute prismatic site of a small (unramified at ) base ring is naturally equivalent to the catego…
Crystalline part of the Galois cohomology of crystalline representations
Abhinandan
For and an unramified extension with perfect residue field, we define a syntomic complex with coefficients in a Wach module over a certain period r…
Image Synthesis Using Spintronic Deep Convolutional Generative Adversarial Network
Saumya Gupta, Abhinandan, Venkatesh vadde +2
The computational requirements of generative adversarial networks (GANs) exceed the limit of conventional Von Neumann architectures, necessitating energy efficient alternatives suc…
Crystalline representations and Wach modules in the imperfect residue field case
Abhinandan
For an absolutely unramified field extension with imperfect residue field, we define and study Wach modules in the setting of -modules for . Our main r…