Domenico Fiorenza - Academia.edu (original) (raw)

Papers by Domenico Fiorenza

We exploit the equivalence between t-structures and normal torsion theories on stable ∞-categorie... more We exploit the equivalence between t-structures and normal torsion theories on stable ∞-categories to unify two apparently separated constructions in the theory of triangulated categories: the characterization of bounded t-structures in terms of their hearts and semiorthogonal decompositions on triangulated categories. In the stable ∞-categorical context both notions stem from a single construction, the Postnikov tower of a morphism induced by a Z-equivariant multiple (bireflective and normal) factorization system {F i } i∈J . For J = Z with its obvious self-action, we recover the notion of Postnikov towers in a triangulated category endowed with a t-structure, and give a proof of the the abelianity of the heart in the ∞-stable setting. For J is a finite totally ordered set, we recover the theory of semiorthogonal decompositions. References 24

We characterize t-structures in stable ∞-categories as suitable quasicategorical factorization sy... more We characterize t-structures in stable ∞-categories as suitable quasicategorical factorization systems. More precisely we show that a t-structure t on a stable ∞-category C is equivalent to a normal torsion theory F on C, i.e. to a factorization system F = (E, M) where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.

We promote geometric prequantization to higher geometry (higher stacks), where a prequantization ... more We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher gauge groupoids and Courant groupoids assigned to a higher prequantization, and establish the corresponding Atiyah sequence as an integrated Kostant-Souriau infinity-group extension of higher Hamiltonian symplectomorphisms by higher quantomorphisms. We also exhibit the infinity-group cocycle which classifies this extension and discuss how its restrictions along Hamiltonian infinity-actions yield higher Heisenberg cocycles. In the special case of higher differential geometry over smooth manifolds we find the L-infinity-algebra extension of Hamiltonian vector fields -- which is the higher Poisson bracket of local observables -- and show that it is equivalent to the construction proposed by the second author in n-plectic geometry. Finally we indicate a list of examples of applications of higher prequantization in the extended geometric quantization of local quantum field theories and specifically in string geometry.

Preprints by Domenico Fiorenza

We develop the theory of recollements in a stable ∞-categorical setting. In the axiomatization of... more We develop the theory of recollements in a stable ∞-categorical setting. In the axiomatization of Beȋlinson, Bernstein and Deligne, recollement situations provide a generalization of Grothendieck's "six functors" between derived categories. The adjointness relations between functors in a recollement D 0

We exploit the equivalence between t-structures and normal torsion theories on stable ∞-categorie... more We exploit the equivalence between t-structures and normal torsion theories on stable ∞-categories to unify two apparently separated constructions in the theory of triangulated categories: the characterization of bounded t-structures in terms of their hearts and semiorthogonal decompositions on triangulated categories. In the stable ∞-categorical context both notions stem from a single construction, the Postnikov tower of a morphism induced by a Z-equivariant multiple (bireflective and normal) factorization system {F i } i∈J . For J = Z with its obvious self-action, we recover the notion of Postnikov towers in a triangulated category endowed with a t-structure, and give a proof of the the abelianity of the heart in the ∞-stable setting. For J is a finite totally ordered set, we recover the theory of semiorthogonal decompositions. References 24

We characterize t-structures in stable ∞-categories as suitable quasicategorical factorization sy... more We characterize t-structures in stable ∞-categories as suitable quasicategorical factorization systems. More precisely we show that a t-structure t on a stable ∞-category C is equivalent to a normal torsion theory F on C, i.e. to a factorization system F = (E, M) where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.

We promote geometric prequantization to higher geometry (higher stacks), where a prequantization ... more We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher gauge groupoids and Courant groupoids assigned to a higher prequantization, and establish the corresponding Atiyah sequence as an integrated Kostant-Souriau infinity-group extension of higher Hamiltonian symplectomorphisms by higher quantomorphisms. We also exhibit the infinity-group cocycle which classifies this extension and discuss how its restrictions along Hamiltonian infinity-actions yield higher Heisenberg cocycles. In the special case of higher differential geometry over smooth manifolds we find the L-infinity-algebra extension of Hamiltonian vector fields -- which is the higher Poisson bracket of local observables -- and show that it is equivalent to the construction proposed by the second author in n-plectic geometry. Finally we indicate a list of examples of applications of higher prequantization in the extended geometric quantization of local quantum field theories and specifically in string geometry.

We develop the theory of recollements in a stable ∞-categorical setting. In the axiomatization of... more We develop the theory of recollements in a stable ∞-categorical setting. In the axiomatization of Beȋlinson, Bernstein and Deligne, recollement situations provide a generalization of Grothendieck's "six functors" between derived categories. The adjointness relations between functors in a recollement D 0