Marta Pérez Rodríguez's research

Research fields

Cohomology of schemes. Algebraic Geometry.

Publications

• Divisores y haces inversibles en esquemas noetherianos
  Álxebra, 64. Universidade de Santiago de Compostela, Santiago de Compostela, 2000. (PDF)
• Geometría infinitesimal de esquemas formales
  Álxebra, 65. Universidade de Santiago de Compostela, Santiago de Compostela, 2004. (PDF)
• Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes (with Leo Alonso Tarrío y Ana Jeremías López) Comm. Algebra, 35 (2007), no. 4, pp. 1341-1367. (PDF)

Preprints

• Local structure theorems for smooth maps of formal schemes (with Leo Alonso Tarrío and Ana Jeremías López).(PDF)
• Basic deformation theory of smooth formal schemes.(PDF)
• The derived category of quasi-coherent sheaves and axiomatic stable homotopy (with Leo Alonso Tarrío, Ana Jeremías López y M� Jesús Vale Gonsalves).(PDF)

Conference talks

• Divisors and invertible sheaves on noetherian schemes
  Géometrie Algébrique en Liberté VIII, CIRM, Luminy (France), March 2000. (PDF)
• On infinitesimal conditions of morphisms on formal schemes
  Géometrie Algébrique en Liberté IX, CIRM, Luminy (France), March 2001. (PDF)
• Pseudo lisitud en extensiones de anillos noetherianos ádicos
  VII Jornadas de Teoría de Anillos, La Coruña (Spain), March 2002. (PDF)
• Pseudo lisitud en esquemas formales
  Métodos Cohomológicos en Geometría Algebraica, Santiago de Compostela (Spain), September 2002. (PDF)
• Esquemas formales lisos
  Workshop on Singularities, Marie Curie HD, Universidad de Valladolid, Sedano (Spain), June 2004. (PDF)

Imparted courses

• "Esquemas formales". Departamento de Álxebra, Universidade de Santiago de Compostela, from March to July 2001.
• "Teoremas de anulación". Departamento de Álxebra, Universidade de Santiago de Compostela, from March to July 2002.

Participation in supported research projects

• 1998-2001. Cohomología de esquemas y categorías derivadas. Ministerio de Educación y Cultura (DGESIC PB97-0530). Head researcher: Leovigildo Alonso Tarrío. (Cohomology of schemes and derived categories)
• 2001-2004. Nuevos métodos en cohomología de esquemas. Ministerio de Ciencia y Tecnología (BFM2001-3241), supported also by Xunta de Galicia (PGDIT 01PX120701PR). Head researcher: Leovigildo Alonso Tarrío. (New methods in cohonmology of schemes)
• 2004-2007. Estructura de las categorías derivadas y cohomología de espacios singulares. Ministerio de Educación y Ciencia (MTM2005-05754), supported also by Xunta de Galicia . Head researcher: Leovigildo Alonso Tarrío. (Structure of derived categories and cohomology of singular spaces)

Research stays

• From September 1999 to October 2000, from March 2001 to July 2001, from March 2002 to July 2002, September 2002, March and April 2004: Departamento de Álxebra, Universidade de Santiago de Compostela (Santiago de Compostela, España)
• From September 2004 to December 2004: visiting scholar. Math Department, Purdue University (West Lafayette, USA).
• February 2005 and from February to May 2006: postdoctoral research position Marie Curie. Laboratoire de Mathématiques, Université Paris XI (Orsay, France).

Attendance to conferences and meetings

• Géometrie Algébrique en Liberté VIII, CIRM, Luminy (France), 27-31 March 2000.
• Géometrie Algébrique en Liberté IX, CIRM, Luminy (France), 19-23 March 2001.
• VII Jornadas de Teoría de Anillos, La Coruña (Spain), 21-22 March, 2002.
• Workshop on Global Geometry of Algebraic Varieties, Universidad Complutense de Madrid, Madrid (Spain), 19-21 December 2002.
• Métodos Cohomológicos en Geometría Algebraica, Santiago de Compostela (Spain),19-21 September 2002.
• Joint Meeting between the RSME and the AMS, Sevilla (Spain), 18-21 June 2003.
• Workshop on Singularities, Marie Curie HD, Universidad de Valladolid, Sedano (Spain), 21-23 June 2004.
• III Seminario de Categorías y Aplicaciones, Santiago de Compostela (Spain),8-10 September 2005.
• ICM Satellite Conference "Algebraic Geometry", Segovia (Spain), 16-19 August 2006.
• International Congress of Mathematicians (ICM), Madrid (Spain), 22-30 August 2006.
• Approaching Mathematics through Algebra, Pontevedra (Spain), 25-29 June 2007.

Attendance to courses and schools

• "Variedades tóricas" imparted by professor Antonio Campillo López from Universidad de Valladolid. Departamento de Álxebra, Universidade de Santiago de Compostela, 8-15 November 1998.
• "Geometric applications of the residue theorem" imparted by professor Reinhold Hübl from Ratisbona University. Departamento de Álxebra, Universidade de Santiago de Compostela,19-27 April 1999.
• "Cohomología cristalina" imparted by professor Adolfo Quirós Gracián from Universidad Autónoma de Madrid. Departamento de Álxebra, Universidade de Santiago de Compostela, 6-11 September 2000.
• "Minimal models and classification of surfaces and higher dimensional varieties" imparted by professor Miles Reid. Departamento de Álgebra, Universidad Complutense de Madrid, 9-18 December 2002.
• "Advanced School in Basic Algebraic Geometry". Courses: Descent (A. Vistoli) Grothendieck topologies (A. Vistoli), Hilbert and Quot schemes  (N. Nitsure, L. Göttsche), Formal existence Theorem for modules (L. Illusie), Picard Schemes (S. Kleiman). Abdus Salam ICTP, Trieste (Italy), 7-18, July 2003.
• "Summer Scool on Symbolic Computation", Santiago de Compostela (Spain),16-21 July 2007.

Seminars

• Participation in the weekly seminar "Cohomología de esquemas", from 2001 to 2004: Departamento de Álxebra, Universidade de Santiago de Compostela. ("Cohomology of schemes")
• Participation in the weekly seminar "Geometría Algebraica", from 1998 to 2001: Departamento de Álxebra, Universidade de Santiago de Compostela. ("Algebraic Geometry")
• Participation in the seminar "Théorie de Dieudonné Cristalline", from February to March 2006: Institut Galilée, Université Paris 13. ("Crystalline Dieudonné Theory")