3 papers
math.AG2018
Connectivity of joins, cohomological quantifier elimination, and an algebraic Toda's theorem
Saugata Basu, Deepam Patel
Let be a non-empty closed subscheme over an algebraically closed field , and $\mathrm{J}^{[p]}(X) = \mathrm{J}(X,\mathrm{J}(X,\cdots,\mathrm{J}(X,X)\c…
math.AG2018
A Kawamata-Viehweg type formulation of the Logarithmic Akizuki-Nakano Vanishing Theorem
Donu Arapura, Kenji Matsuki, Deepam Patel +1
In this largely expository article, we present a Kawamata-Viehweg type formulation of the (logarithmic) Akizuki-Nakano Vanishing Theorem. While the result is likely known to the ex…
math.LO2018
VC density of definable families over valued fields
Saugata Basu, Deepam Patel
We prove a tight bound on the number of realized patterns (or equivalently on the Vapnik-Chervonenkis codensity) of definable families in models of the theory of algebraicall…