Sylvain Brochard

activity

20092025

most citedFiniteness theorems for the Picard objects of an algebraic stack

15 citations · 39 across the 7 of their papers we have counts for

collaborators

9 papers

math.AC2025

A freeness criterion for complexes with derived actions

Sylvain Brochard, Srikanth B. Iyengar, Chandrashekhar B. Khare

Inspired by the patching method of Calegari and Geraghty, and a conjecture of de Smit that has been proved by the first author, we present a conjectural freeness criterion without…

math.AC2022

Independent sequences and freeness criteria

Sylvain Brochard

Let $M$ be a module over a Noetherian local ring $A$ . We study $M$ -independent sequences of elements of $m_{A}$ in the sense of Lech and Hanes. The main tool is a new char…

math.NT2021

Wiles defect for modules and criteria for freeness

Sylvain Brochard, Srikanth B. Iyengar, Chandrashekhar B. Khare

F. Diamond proved a numerical criterion for modules over local rings to be free modules over complete intersection rings. We formulate a refinement of these results using the notio…

math.AC2020★ 5 cited

A freeness criterion without patching for modules over local rings

Sylvain Brochard, Srikanth B. Iyengar, Chandrashekhar Khare

It is proved that if $φ : A \to B$ is a local homomorphism of commutative noetherian local rings, a nonzero finitely generated $B$ -module $N$ whose flat dimension over $A$ is at…

math.AC2016★ 7 cited

Proof of de Smit's conjecture: a freeness criterion

Sylvain Brochard

Let $A \to B$ be a morphism of Artin local rings with the same embedding dimension. We prove that any $A$ -flat $B$ -module is $B$ -flat. This freeness criterion was conjectured by de…

math.AG2016★ 7 cited

Morphisms of 1-motives defined by line bundles

Cristiana Bertolin, Sylvain Brochard

Let $S$ be a normal base scheme. The aim of this paper is to study the line bundles on 1-motives defined over $S$ . We first compute a dévissage of the Picard group of a 1-motive $M…

math.AG2014

Duality for commutative group stacks

Sylvain Brochard

We study in this article the dual of a (strictly) commutative group stack $G$ and give some applications. Using the Picard functor and the Picard stack of $G$ , we first give some s…

math.AG2012★ 5 cited

Topologies de Grothendieck, descente, quotients

Sylvain Brochard

In this note, we present a few existence theorems for the quotient of a scheme by the action of a group. The first two sections are devoted to Grothendieck topologies and descent t…

math.AG2009★ 15 cited

Finiteness theorems for the Picard objects of an algebraic stack

Sylvain Brochard

We prove some finiteness theorems for the Picard functor of an algebraic stack, in the spirit of SGA 6, exp. XII and XIII. In particular, we give a stacky version of Raynaud's rela…