BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news1990@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20260402T095457 DTSTART;TZID=Europe/Zurich:20260407T103000 SUMMARY:Seminar Algebra and Geometry: Elyes Boughattas (Université de Renn es) DESCRIPTION:A starting point of arithmetic is to solve diophantine equation s over the field Q of rational numbers. More generally\, given an algebrai c variety over Q\, can we say whether it has a rational point? Local-globa l principles are a well-known strategy to tackle this question. For exampl e\, is the existence of solutions over Q implied by the existence of solut ions over all completions of Q? The first non-examples to this question ha ve been found in the 1960's. Then Manin introduced in 1970 a cohomological obstruction\, called the "Brauer-Manin obstruction" which is conjectured to explain the lack of rational points for the nice family of rationally c onnected varieties.\\r\\nThe fibration method is a conjecture which predic ts that the Brauer-Manin obstruction behaves well for families of varietie s parametrised by the projective line. During the last ten years\, this co njecture has known a new impetus\, after the foundational works of Harpaz and Wittenberg. As an example\, a geometric consequence of this conjecture in characteristic p\, is that families of Severi-Brauer varieties paramet rised by the projective line should be unirational.\\r\\nDuring this talk\ , I will present a work in progress where I prove an analogue of the fibra tion method over function fields of curves over finite fields. This boils down to the study of explicit moduli spaces of curves on surfaces over fin ite fields. X-ALT-DESC:

A starting point of arithmetic is to solve diophantine equati ons over the field Q of rational numbers. More generally\, given an algebr aic variety over Q\, can we say whether it has a rational point? Local-glo bal principles are a well-known strategy to tackle this question. For exam ple\, is the existence of solutions over Q implied by the existence of sol utions over all completions of Q? The first non-examples to this question have been found in the 1960's. Then Manin introduced in 1970 a cohomologic al obstruction\, called the "Brauer-Manin obstruction" which is conjecture d to explain the lack of rational points for the nice family of rationally connected varieties.

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The fibration method is a conjecture which p redicts that the Brauer-Manin obstruction behaves well for families of var ieties parametrised by the projective line. During the last ten years\, th is conjecture has known a new impetus\, after the foundational works of Ha rpaz and Wittenberg. As an example\, a geometric consequence of this conje cture in characteristic p\, is that families of Severi-Brauer varieties pa rametrised by the projective line should be unirational.

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During th is talk\, I will present a work in progress where I prove an analogue of t he fibration method over function fields of curves over finite fields. Thi s boils down to the study of explicit moduli spaces of curves on surfaces over finite fields.

DTEND;TZID=Europe/Zurich:20260407T120000 END:VEVENT END:VCALENDAR