**SCHOOL (AND WORKSHOP) ON
**

**THE GEOMETRY OF ALGEBRAIC
STACKS
**TRENTO, SEPTEMBER 1-6,
2008

**
**First announcement

**Lecturers.
**

B. Fantechi(SISSA, It)A. Kresch(Universität Zürich, CH)

Supporting lectures will be delivered by

**Organizers.
**The School/Workshop is organized by G. Casnati, C. Fontanari, R.
Notari, M.L. Spreafico. For contacting the organizers send a mail
to

**Aim of the School.
**

The School is mainly aimed to Phd students and young researchers
in Algebraic Geometry, introducing the participants to research,
beginning from a basic level with a view towards the applications and
to the most recent results.

A tentative program is as follows.

Motivation: why stacks are needed. Basic example: moduli of curves of
genus g. The 2-category of groupoids, schemes as functors, categories
fibered in groupoids, pseudofunctors. The stack condition.
Representable morphisms, definition of algebraic stack (in the sense
of Deligne-Mumford). Quotient stacks, stacks associated to groupoids.
The 2-category of stacks; open, closed substacks; topological space
associated to a stack. Properties of stacks and of their morphisms;
valuative criteria for separatedness and properness. Inertia stack.
(Quasi)coherent sheaves on a stack, cohomology of sheaves. Main
worked out examples: moduli of stable pointed curves, moduli of
stable sheaves, weighted projective stacks and toric DM stacks.
Infinitesimal study of moduli stacks and deformation theory. A short
introduction to Artin stacks will also be provided.

**Further announcements.**

A more detailed second announcement (containing informations on
accomodation, registration and financial supports) will follow
probably in February 2008.