Higher Structures in Arithmetic Geometry
Four foundational mini-courses, invited research talks, and a dedicated student poster afternoon, organized within the framework of the REMOLD doctoral network.
Summer school page →Intensive research period · Spring 2027
A Special Trimester in Arithmetic Geometry
A research program at the University of Milan bringing together long-term visitors, PhD courses, weekly seminars, and four international conferences.
- Dates
- April – July 2027
- Host
- Department of Mathematics “Federigo Enriques”
- Location
- University of Milan · Milano, Italy
The trimester
Research across modern arithmetic geometry
The program connects arithmetic geometry with p-adic Hodge theory, L-functions, motivic homotopy theory, algebraic K-theory, and higher and derived methods.
Long-term visitors will take part in two regular weekly seminars — a study seminar open to PhD students and a research seminar — interact with the local community, and contribute to training activities for early-career researchers. Four conference weeks provide concentrated opportunities for lectures, discussion, and new collaborations, and two 20-hour PhD courses run between them.
Preliminary information. Speaker lists, detailed schedules, and timetables will be announced as they become available. Registration for each event, and information about support for junior participants, is collected on the registration page.
At a glance
Calendar
Provisional. Dates and venues for individual events are confirmed on the corresponding pages.
April 2027
Program opens Arrival of the first long-term visitors; weekly study and research seminars begin.
Ongoing
Higher Structures in Arithmetic Geometry REMOLD summer school: mini-courses, invited talks, student posters.
Summer school
New Perspectives in Arithmetic Geometry Research conference on p-adic and arithmetic geometry.
Conference
The Arithmetic of L-functions Research conference; preliminary speakers announced, venue TBC.
Conference
Dates TBC
Arithmetica Transalpina — 8th edition Confirmed to take place; all other details still to be announced.
Conference
Dates TBC
PhD courses Two thematic courses, by Shuji Saito and Juan Esteban Rodríguez Camargo.
Training
Four focused events
Conferences and school
Each event has its own page, so that schedules, abstracts, registration links, and practical information can be added without changing the structure of the site.
New Perspectives in Arithmetic Geometry
Recent developments in p-adic and arithmetic geometry, with an emphasis on cohomological methods, rigid and adic geometry, and related interactions.
Conference page →The Arithmetic of L-functions
A conference on L-functions, Euler systems, and algebraic cycles. Preliminary speakers are listed on the conference page; venue to be confirmed.
Conference page →Arithmetica Transalpina — 8th edition
Confirmed to take place as part of the trimester. Dates, venue, organizers, and scientific program will be announced.
Conference page →Confirmed
Long-term participants
These participants will spend an extended period at the Department and will contribute to the trimester through research interactions, seminars, and training activities. Further names will be added as visits are confirmed.
Adel Betina Besançon
Tess Bouis IAS (Princeton) / IHES (Bures-sur-Yvette)
Pierre Colmez Sorbonne / CNRS
Veronika Ertl Caen
Martin Gallauer Warwick
Lucas Gerth Sorbonne / CNRS
Eyal Goren McGill
Adrian Iovita Concordia
Wiesia Nizioł Sorbonne / CNRS
Asbjørn Nordentoft Copenhagen
Kartik Prasanna Michigan
Shuji Saito University of Tokyo
Training program
PhD courses
Two thematic courses for PhD students will run during the trimester. Dates, rooms, and registration details will be posted when confirmed.
Course I
Étale and tame cohomology, from algebraic to rigid geometry
Shuji SaitoUniversity of Tokyo
This PhD course explores étale and tame cohomology, tracing their development from classical algebraic geometry to modern rigid analytic geometry. It begins with the foundational properties of the étale site, covering classical results.
Addressing the pathological behaviour of étale cohomology for p-torsion sheaves in positive characteristic, the course then introduces the tame site, which resolves these structural deficiencies by suppressing wild ramification. Finally, these tools are applied to rigid analytic varieties and adic spaces.
Course II
Derived Tate adic spaces and analytic D-modules
Juan Esteban Rodríguez CamargoUniversity of Bonn
Applying the new theory of analytic stacks of Clausen and Scholze, the course introduces a general notion of derived Tate adic spaces. This formalism is used to define the analytic de Rham stack in rigid geometry, extending the theory of 𝒟̂-modules of Ardakov and Wadsley to the theory of analytic D-modules.
Foundational results will include the existence of a six-functor formalism and Poincaré duality for analytic D-modules, generalizing previous work of Bode. Finally, the course relates the theory of analytic D-modules to previous work of the speaker with Rodrigues Jacinto on solid locally analytic representations of p-adic Lie groups.
Practical information
Visit and contact
Most trimester activities are hosted by the Department of Mathematics “Federigo Enriques”. Event-specific venue information appears on each conference page.
Department
Dipartimento di Matematica “Federigo Enriques”
Via Cesare Saldini 50
20133 Milano, Italy
Scientific contact
Useful links
The special trimester is supported by the Department of Mathematics “Federigo Enriques” of the University of Milan through the Italian Ministry of University and Research “Dipartimenti di Eccellenza” programme, with additional support from the European Doctoral Network REMOLD.