arXiv subjects

Arnav Tripathy

Publications and source records attributed to Arnav Tripathy.

20 records · Page 2Linked to original sources

arXiv2016

Further counterexamples to the integral Hodge conjecture

We study the integral Hodge conjecture in complex codimension $2$ and $3$ for approximations to the classifying space of groups of type A. In degree two, we prove a conjecture of Ben Antieau, extending his two counterexamples to a general family of groups. In particular, when reduced to a finite field, these spaces extend Antieau's counterexamples to the integral $\ell$-adic Tate conjecture from the cases $\ell = 2, 3$ to all primes $\ell$.

math.AG↗

arXiv2015

The symmetric power and étale realisation functors commute

We show that under mild hypotheses on a proper algebraic space $X$, the functors of taking its symmetric powers and its étale realisation commute up to weak equivalence. We conclude an effective version of the Dold-Thom theorem for the étale site and discuss the stabilisation results for the natural morphisms of étale homotopy groups $π_k \mathrm{Sym}^n X \to π_k \mathrm{Sym}^{n+1} X$ in the context of the Weil conjectures.

math.AG↗